No US administration has ever vowed to annihilate Iran.
American citizens don't chant anti-Iranian slogans on the streets. Iranian flags aren't being burnt in America, and there's hardly any animosity from American citizens towards the Iranian people.
The US doesn't keep Iranian hostages for no good reason.
Other than preventing the people who chant "death to America" from acquiring the capabilities to do so, has the US done anything that poses a threat to Iran?
The CIA had an Iranian PM removed in a coup in 1953. The venal, sordid and unedifying reason? A dispute about oil royalty payments.
It also supported the Shah, which had a rather notorious secret police, all the way up to his removal in 1979.
On top of that, the faction that gained control after the revolution was a rather rabid form of Shiite Islam.
The US has sponsored a long list of sanctions against Iran, had minor armed skirmishes with it, backed its regional rivals and generally opposed it much of the time.
Last, when Iran signed the JCPOA, the USA rather unilaterally broke that deal.
US politicians vie with each other not to be called "soft on Iran".
One doesn't have to be a great fan of Iran to understand why those two don't get along.
There's a long list of Iranian misdeeds at the companion question but those aren't directly relevant to why Iran doesn't like the US except for them being two ideologically opposed systems - a nominally secular Christian democracy vs a nominally democratic Islamist dictatorship (with one of the nominals "weighing" more than the other).
p.s. My own take is that current-government Iran is a place where young women get beaten to death by the police for their choice of clothing. So, no, this answer is not written out of great sympathy for Iran, it merely lists the reasons Iran doesn't like the US, from the point of view of Iran, as asked in the question.
p.p.s. And, no, these aren't all 70 years ago events ;-)
No US administration has ever vowed to annihilate Iran.
Sure, but the [current] US administration essentially supports "regime change" over there.
“Don’t worry, we’re gonna free Iran,” President Joe Biden said [...]
Funnily enough, the previous administration--which imposed the "strongest sanctions in history"--claimed they didn't want regime change, but Iran probably took actions into account louder than words. Also, during the Bush administration, the Iran Freedom and Support Act was passed--essentially funding Iranian opposition to the regime.
The (Trump era) "maximum pressure" sanctions are similar to what was imposed on North Korea (prior to Russia's invasion of Ukraine). No other countries had to move dollars by suitcases. So, expect a North Korea & Russia level of "love" for the US, just based on that.
Iranian leaders surely resent the continued US influence/presence in Iraq, which they almost certainly regard based on (Shia) religion as much closer to them--essentially their "rightful sphere of influence"--even if officially they use terms like brotherly love. (Compare with Russia's complaints about NATO/EU influence in countries on their border. Lately, Iraqi leaders are busy condemning 'round-the-clock both the US and Iran for violating their sovereignty.)
And Iraq is a somewhat more complicated affair than that. People sometimes forget that Iran has had repeated conflicts with Kurdish separatists who take refuge in Iraq, so in that regard the US support for the [Iraqi] Kurds in particular is resented in Iran, probably as much as Turkey resents US support for [Syrian] Kurds. (And Iraqi Kurdistan is also where most ordanced fired from Iranian land[ed], and not just recently.)
Fact of the matter is that relations have (mutually) spiraled down.
There are multiple reasons why the Islamic Republic doesn't like the US and the West in general. Usually the role CIA played in the 1953 coup is considered as the main reason, but it isn't. The Islamic Republic doesn't like Mossadeq and the National Front either. Before the revolution they worked together to topple the Shah, after the revolution, some members of the National Front(the party that was implicated in the 1953 coup), were in the government but they were soon marginalized.
Pahlavi dynasty reigned in Iran from 1925 to 1979 and had two monarchs: Reza shah(1925-1941) and Muhammad Reza shah(1941-1979). Reza shah, the founder of the dynasty was removed from power in 1941 when Iran was occupied by Allies during the WWII and his son Muhammad Reza became the monarch and he was a close ally of the US and the West. There were two main opposition groups under Pahlavis: communists and Islamists, communists represented intellectuals of the time and Islamists represented the mass, the majority of Iranians in a traditional conservative country.
Another factor that contributed to the anti-American sentiment was the 1953 coup. In 1953 Mossadeq, the then prime minister wanted to restrict the power of the Shah(the monarch), things were going on well for Mossadeq and even they thought that everything was finished, but a group of Iranian generals with the support of CIA managed to change the situation, Mossadeq's government fell only after three days and he was put under house arrest. This coup intensified the anti-American sentiment among Iranian intellectuals(mainly communists).
Anyway, they toppled the Pahlavi dynasty in 1979, and the interim government was composed of both groups: Islamists and leftists, during this period Khomeini needed those intellectuals to communicate with the world and form a new government.
A year after the victory of the revolution, the system was working and they didn't need leftist and intellectuals any more(those who saw the US as imperialist power). They were dismissed and marginalized and were purged in 1988. The Islamic Republic formed a homogenous conservative government. During this period left wing groups, main reason of anti-Americanism, weren't in the government any more, but they remained anti-American, probably because they need an enemy to blame for their failure. Anyway they need a pretext to convince their supporters. Now those who still support the Islamic Republic in Iran blame the US for economic problems caused by sanctions without knowing that the animosity began in 1979 after the hostage crisis by the Islamic Republic.
Besides, the Islamic Republic has other reasons to hate the US and the West: they talk about democracy, they finance media outside Iran that provide information to Iranians(who otherwise were limited to the regime's media), they give political asylum to opponents and finally they have contributed to the overthrow of regimes in many neighbouring countries such as in Afghanistan, Iraq and Libya.
In short, the anti-American sentiment in Iran began by left wing groups and communists in 1940s, it was intensified by the coup in 1953 and was adopted by the Islamic Republic that, like all authoritarian regimes is afraid of the free world.
There is a misunderstanding in this question which I address here:
Americans don't chant in the streets death to …
Note that the intention of Iran is not the American people, but the government, the Senate and the actors behind the scenes of US such as lobbyists.
No US administration has ever vowed to annihilate Iran.
AFAIK Iran never vowed to annihilate US but some of US officials and businessmen offered similar thing. Lindsey Graham says US should bomb Iran (many times). Sheldon Adelson calls on US to nuke Iran.
Why does the I.R. Iran view the US as its principal geopolitical adversary in the world?
Iranians believe It is known that the Mossad and the CIA supplied torture tools to SAVAK (the secret police of the Shah) and trained SAVAK officers (SAVAK Formed almost 3 years after 1953 coup d'état). SAVAK's tortures were the worst and most inhumane possible and the most barbaric methods of torture the world has ever seen, which many consider to be the beginning of Iranians' hatred of US (and Israel). See this and this.
This is one of the important and unforgettable parts of Iran's history and for this reason the SAVAK torture center has been turned into a museum since 2002. (see also this (graphical)) A prison museum that recalls a slice of the tragic and painful history of its prisoners for visitors by featuring the sculptures of torturers, prisoners, and different methods and devices of tortures that shock every visitor.
After Iran Revolution, and Saddam invasion of Iran, at United Nations' press conference the PM of Iran, Mohammad Ali Rajai, who went to the UN directly from the war front, displayed his bare feet on the table in front of the world's media cameras and said (perhaps in response to a question about US hostages):
"I was in the prisons of the Shah regime and imprisoned by Carter and America for two years. After four years, the effects of torture and hardships that were inflicted on me in prison are still visible on my body. For two years, I felt Carter's whips on my feet, and we are treating the hostages in the Spy Den (US embassy) completely humanely."
After this speech, UN suspended Iran's officials from UNGA for 7 years. Mohammad Ali Rajai was martyred in MEK terrorist group bombing.
Here are some important US actions against Iran:
and etc. that is just part of US actions against Iran. There are also many other reasons e.g. Anti-Iranian Hollywood movies, supporting separatist terrorist groups, US seizing Iranian oil cargo etc. that I think it is more than enough for Iran to view the US as its principal adversary.
I accidentally found the exact same question in CIA documents:
… Why do so many Iranians believe in U.S. complicity, guilt? Why do they so fervently endorse the anti-American Khomeini and the holding of the hostages? Of course, we know the embassy takeover was triggered by the Shah's entry into the U.S. last October for medical treatment. More about that later. But beyond that, the fury in Iran focuses on the undenied fact that the CIA restored the exiled Shah to the Peacock Throne back in 1953. And after that, the Iranians have been told, the CIA helped the Shah set up SAVAK, the secret police force that has tortured so many thousands of them. A classified Senate Foreign Relations Committee report confirms the CIA's role in forming SAVAK. It says the CIA provided the Shah money, as well as training, for that purpose. Of course, the brutality came later. …
See e.g.:
You can see a long list of mutual grievances on Wikipedia.
In addition to all the political stuff like sanctions, military actions, and spy shenanigans that hurt the Iranian people which the US has endorsed that other answers have discussed, there is an additional reason that none of the other answers have addressed: the immorality of US popular culture.
From LGBT issues to feminism, the promotion of divorce, and the destruction of traditional gender roles, the US promotes a moral stance that is fundamentally opposed to the Islamic moral code the Iranian government promotes.
Many have posted good arguments here, I will just add that Iran has oil.
If we look at America's history of invading countries with oil and installing puppet governments so they can steal the oil, any country with oil that they don't simply hand over to the West (like Nigeria) should be a bit nervous.
