The following is probably correct, in a cognitive, psychological way:
to be able to create good humour one must have a sense and
appreciation for good humour
However, I don't think the expression, to have a sense of humor is motivated by that logic. I perceive that to have a sense of humor is just as likely to refer to the ability to be humorous as to be appreciative of humor. In other words, having a sense of humor is used to describe someone who says funny things, but also to describe someone who responds favorably to funny things. This may be an instance of American English. I'll cite part of a prior EL&U SE question
What is a dry sense of humor? for corroboration:
Developing a dry sense of humor can be challenging and fun....Every
time I employ my dry wit, I get many different reactions.
Note in particular the answer, which is consistent with my understanding of this expression, as I described above:
dry... (of a joke or sense of humor): subtle, expressed in a
matter-of-fact way... "he delighted his friends with a dry, covert sense of
humor"
Additional confirmation is provided by an excerpt from both title and content of this eHow article, How to Improve Your Sense of Humor
...why people don't consider you "funny." You may discover
that it's just your timing or delivery... your jokes [may be] so
off-color, unusual or offensive that the general "audience" doesn't
appreciate them.