I'm not sure I can explain it very well, but it's simply the "acquired" but you mentioned already. Through repeated exposure, you can make yourself come to like or accept a particular taste you didn't like before.

Traditionally "bad" tasting things like coffee and beer are a good example I think. At first, hoppy or bitter, we don't like it, but the more it is tried, and the different types we try, the more flavours we learn to detect and appreciate, going back to the original, you may find you taste something completely different, or you just started on something bad in the first place.