It is possible that it's just plain ol' stubborness, but I agree that every effort should be made to make sure he isn't hurting somewhere.
One time I rode my horse up a really challenging, steep trail and I felt bad because he wasn't in good enough shape for it (I didn't know what I was getting myself into). Because I felt bad, I was letting him stop and take breaks quite often, and sometimes I even let him stop when he felt the need.
After that one incident, he became balky about going up hills. Only steep ones, but I could bet on him digging his heels in about going up hills until I really forced the issue.
I had a professional circle y saddle rep/fitter fit my horse so I was confident with saddle fit. Had the horse vetted on numerous occasions. The horse was perfectly sound in every way as far as anyone could tell.
He eventually got better about it, but I truly believe after that bad experience with going uphill he got sour about it.