First off, I don't think anyone needs to be able to explain why they like or dislike something. However, if someone wants to be able to have an intelligent conversation with someone else about the merits or faults of a particular piece of art -- be it a movie, a novel, a poem, a painting -- the ability to deconstruct the thing in question is essential. Simply saying "I like/disklike this thing because I do" doesn't exactly allow room for discussion.
I also disagree that analyzing something changes one's emotional reaction to it. Rather, I think that being analytical helps one understand why they feel as they do. If a person's appreciation for something changes as a result of analyzing it, then I'd say that person A) forms judgements very quickly with little thought or B) is easily persuaded.
Being an English teacher, I've spent the better part of my academic life learning how to analyze literature, and now I spend my working life teaching others to do the same. Like many students, I went through my phase of thinking 'why do we have to analyze everything? Can't I just read a book and enjoy it without having to think about it?' However, in retrospect, I'm glad I learned to be analytical as it has actually made me more appreciative of things like novels and films. Now, when I see a movie, I don't just say to myself, "Well, that was cool." Instead, I can say, "Wow, I like that movie because of its character arcs, its themes, its symbolism" and so on.
I say all this in light of having this very kind of discussion with a friend over the weekend. We were discussing the movie Unbreakable which I love but he hates. If I had simply said, "I like it because I like it," and he responded, "Oh yeah? Well I hate it because I hate it," we wouldn't have had very much to talk about. Instead, we each considered the other's arguments and insights. At the end of the day, his hearing why I love the movie and my hearing why he hates the movie didn't change the other's opinion, but it allowed us to understand the each other's (and our own) reaction better.