I often hear from exhausted parents that their child is potty trained to urinate in the potty yet won't have BM's in the potty.
Usually this is a control issue and it's sometimes related to things going in in the family, For instance, an addition of a new baby to the family could be at the root of it. Many well meaning parents want to get the first born completely potty trained by the time the baby arrives. That can put a lot of pressure on both parents and child.
I often tell parents that when a second child enters a family the first-born views it much like you would if your spouse said, "Honey, things between us are really great, but another woman/man is going to be moving in with us. She/he will be so much fun and you can do things together." Your response would probably be "I don't think so!" Your first-born has no control over a baby entering the family but he can control his BM's.
Parents resort to begging and bribing the child to go poop in the potty. This is giving your child negative attention and he's taking advantage of it. The more you push the more he's going to want to take control and then you've got a battle of wills.
Some parents will try to reason with their young child and ask them repeatedly why he doesn't want to poop in the potty. A child of three or four really doesn't know the answer to that question because they're not developmentally able to be rational about this like an adult.
When potty training has become a war between parent and child I suggest parents stop pushing. That will lessen the child's need to control the situation and reduce everyone's stress. He'll do it when he's ready.
Also ask yourself if you're giving your child enough positive attention. That may be what he's seeking because because by controlling his BM's he's certainly got your attention.