One quick hint is its original links to the Muslim Brotherhood in Egypt.
Hamas was established in 1987, and has its origins in Egypt's Muslim Brotherhood movement, which had been active in the Gaza Strip since the 1950s and gained influence through a network of mosques and various charitable and social organizations. In the 1980s the Brotherhood emerged as a powerful political factor, challenging the influence of the PLO,3 and in 1987 adopted a more nationalist and activist line under the name of Hamas.3 During the 1990s and early 2000s, the organization conducted numerous suicide bombings and other attacks against Israel.
The Muslim Brotherhood is a group really loathed by Egypt's government and in fact used to justify the re-coup in 2013 by Egypt's military to put Sisi in charge after the Arab Spring takeover.
There were mixed international reactions to the events.[13][14] Most Arab leaders were generally supportive or neutral, with the exception of Qatar and Tunisia who strongly condemned the military's actions. The US avoided describing the action as a coup.
(the irony being, IIRC, that the Muslim Brotherhood wasn't doing that well in governance and were quickly outliving their welcome with the Egyptian public)
Egypt's government is not atypical of other governments of the region: nominally pious, democratically poor and fairly corrupt and inept economically. Whether or not the Muslim Brotherhood would do better in day to day affairs is uncertain, but they have ample grounds to criticize and that scares the governments in question because they have limited legitimacy towards their people.
Or look at the tug of war in popularity between the PA and Hamas: Hamas may suck, but some aspects of it do appeal to large parts of the Arab electorates: their current governments leave much to be desired, so any change is seen as good.
The Middle East is full of tensions between democracy, dictatorship and religious fundamentalism. See also the Algerian Civil War in the 90s. The Syrian Civil War and its antecedents under Assad Senior - the siege of Hama, against the Muslim Brotherhood, in 1982, allegedly 20000+ civilians killed.
As noted in a comment, Hamas' cozy if complex relationship with Iran - the link here is fairly elaborate in its analysis - really doesn't sit well with the most of the Arab governments either.
While in the past Hamas has set aside its allegiance to the Muslim Brotherhood and its core Sunni teachings to reach out to Shi’a Iran for tactical support, it may now turn to Tehran to help ensure its very survival in the face of an Israeli military campaign aimed at wiping the group out. Tehran would welcome a stronger partnership with Hamas for utilitarian reasons, as it has long depended on its network in the Arab world to export a distinctly Iranian Islamic revolutionary agenda abroad.
In the Syrian Arab Spring of 2011, Hamas and Tehran parted ways due to the group’s opposition to Iranian-backed President Bashar al-Assad, who was fighting Sunni rebels; and a year later, Hamas relocated its headquarters from Syria to Qatar. But that decision was not final, and for some time, the Palestinian militant group seemingly vacillated on whether to embrace fresh ties with Iran, particularly while most Sunni Arab governments remained opposed to Assad. Illustratively, Hamas political bureau head Ismail Haniyeh traveled to Tehran in early 2012 to meet with Iranian leaders, who insisted on aligning the interests of Palestinian and non-Palestinian militant groups such as Hezbollah.
The threads of Iran’s cooperation with Hamas emerged more clearly in later years. During the 2006 Israel-Hezbollah war, Gadhafi supported Hezbollah against Israel. But when he was ousted from power in the 2011 Libyan Arab Spring, Tehran confirmed it had secretly forged ties with his opponents to help overthrow him through connections with the Libyan branch of the Muslim Brotherhood.
That article may be understating their links, but seems more insightful than regurgitating US State Dept's analysises (it is a massive data dump). In any case, any whiff of Tehran is going to be upset regional powers. And, yes, Iran => Persian, rest => Arab. But also, Iran => Shiite, rest => Sunni. Which also affects Hamas - Iran relations. Note that the Muslim Brotherhood however is very much a Sunni affair.
Last... "the West". Hamas is certainly in opposition to "the West". But some Arab governments are seen by some of their population as too Western-leaning (remember Bin Laden's diatribes against Saudi). That's another vulnerability perceived by these governments. The rather complex attitudes of Western countries towards Arab democracy - "well, it has to be the right kind of democracy, you know", muddy those waters even more.
