Maybe I'm not getting the question completely, but the answer seems straightforward to me:
isn't it fallacious for some to say "X is better than Y because I like X more"
Yes, this is fallacious. Everybody is 100% entitled to say "I like X more than Y". That is a statement that is not attackable. No statement about our internal state of mind can be attacked in any way. Even if someone thinks the statement is a lie, there is no way for them to prove it. The objective, physical representation of "I like ..." (i.e., an emotion about two objects) lies within our brain matter, and so far we have no way whatsoever to read that, except by the individuum making statements.
By the very same token, whether an individual likes or dislikes something has absolutely no impact on reality. If one person likes something, or a billion persons, makes no difference whatsoever to the objective value of a thing, generally speaking, although there might be correlation or mild causation of course.
As an example: for the sake of argument, let's assume that there is some dish which is weird and rare, and is unknown to many people (say snails, raw insects, Surströmming, whatever). Do a tasting where a person gets an absolutely delicious but cheap dish (say, chocolate ice cream with strawberries) on the one hand, and said weird dish in the other. You can readily expect that 99% of all judges would rate the ice cream much higher than said other dish.
At the same time, you have a select minority of people who - say - through knowledge of the cultural history and importance of the "bad" dish, compared with its rarity, indeed do value it higher than the ice cream! In fact, since the ice cream is ubiquitous and cheap, it is worth little to them. And even if the other dish is indeed an acquired taste, the person might pay tenfold for the specialty, or cherish the day when they got a chance to taste it (even if at no cost).
To cut to the chase: for the sentence "X is better than Y" to make sense, you need some kind of metric. You absolutely can come up with all kinds of metrics, but unless you are in fact interested the metric of "how many people say they like X vs Y" (which would make perfect sense - we do it all the time, in marketing, democracy etc.), "liking" in the form of an individual opinion is utterly inconsequential for "worth relationships".
To answer the question from the title:
Can art be rated objectively
Yes, of course, simply by defining what you mean by "rating". A trivial rating would be "how much does it cost" and just define that the cost of a piece of art is its worth. This immediately and trivially makes all art pieces comparable. Whether you like this kind of rating is secondary. You can come up with others - for example you could decide to measure how difficult a piece of art is to make, or any other objective measurement.
(N.B. obviously using the price as a measure for the value of art is just an exaggerated example here. There are plenty of works of art that fetch millions in auctions which I would never hang up in my home even if someone gave it to me as a gift, because I just don't like them!)
1-How can one avoid this "come back to the argument beginning without proving anything"
Simply force people to make clear whether they mean "X is good" or "I like X". Everybody is entitled to the latter statement. The first one requires a definition of what "good" means. In practice, in my experience, in 99% of cases where people say "X is good", they actually mean "I like X".
Me: "X is good"
You: "X is bad"
-> This is a common cause for strife.
Me: "I like X"
You: "I like Y"
-> This is just an enjoyable chat about personal preferences.
To avoid issues, whenever you actually mean that you like X ore than Y, say so. Avoid objective statements where there is not a clear metric.
2-in terms of objectivity and subjectivity in art
The same: objective descriptions need a formal, measurable, neutral definition. Subjectivity is free-for-all, in a sense the total opposite to the previous.