Why doesn't my baby enjoy tummy time?

My fella didn't start enjoying tummy time until he was about 4 months old. He did the exact thing that you are describing. I think that it was just unfamiliar and uncomfortable. I just made sure to diligently keep putting him on his belly to keep working those muscles. And so he would keep crying. I discovered that if I let him cry it out (only about a couple of minutes when he was about 3.5 months) while talking to him quietly and touching him, he would settle down fairly quickly. Once he stopped crying, I'd roll him over and we would play. Now that he can roll from back to front (he's almost 5 months), the belly is the only way he wants to be, and I'm thankful that he had that belly time because he seems stronger for it.