Actively trying to like something is already a sign that you don't like it intrinsically. Continuing to try strikes me as...some expression of over-socialization. It's okay to pursue things you actually like for your own sake.
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Also, "liking something intrinsically", what does that even mean?
I've learned that liking things behaves a lot like attraction. It has no reasoning or logic, it happens organically, and when you know, you know. Thus, I would never deign to pretend to like something I've found I don't.
Your mileage seems to vary, but I find that for food and drinks in particular it's the acquired tastes you get the most enjoyment from in the end -- I haven't met many people who enjoyed their first glass of peated whisky, for example. Heck, even my best friends are definitely an "acquired taste", as is obvious to me when I introduce them to other people I know.