It is perhaps a case of using a bad example, but that example doesn't need the comma because the two parts are closely related. It's just a short list of what two different people like.

When the independent clauses are not as closely related as that then the comma is (most often) necessary.


There are times when the use of a comma is a style choice and there isn't a right or wrong answer. I would argue that the example given is such a time.

The problem with the grammar and punctuation "rules" we are taught at school is that they are usually only half the story. It's easier to teach that it's "I before E except after C" than "I before E except after C in words that rhyme with "ee" because children will remember the shorter one more easily. The problem is that then people think there are more execptions than the "rule" and thus think that rules are pointless in English. I think a similar problem has happened with the guidelines surrounding the use of commas.