My daughter - she trained in 2 days, no problem peeing in potty, went right to underwear, but wouldn't poop in the potty no matter what! She wanted a pull-up and would only go in one. UGHHH! I tried EVERYTHING, bribes, rewards, etc. I went back and forth between "no pressure, honey" and "this is gross!" but it didn't matter. Every time I tried to encourage her, it ended up in a fight. Easier said than done, but I bit my tongue and backed off.
She would never really articulate "why" and I think it was some fear, but also some stubbornness. One of the big issues was that she always pooped standing up and really wasn't comfortable sitting. We tried major and minor bribes and nothing seemed to work. She would cry and scream and have such a fit! She was really frightened and upset. She never pooped in her undies, though. She would hold it forever. So the idea of just "not giving her a diaper" or saying "we ran out" didn't work for us. She'd hold it for so long that we'd end up with a very constipated kid and it'd hurt when she finally did poop - 4 days later!
SO - here are my 2 BIG RULES: no pooping in underwear, no pooping anywhere but the bathroom!! First, we said she had to go into the bathroom - that's where people poop - not grunting in the corner of the living room... (why do people let their kids do that? lol) She would go to the bathroom, I'd help her put on a pull-up and she'd stay in the bathroom and do her business. So she had to miss out on whatever else was going on - playing, etc. She was not allowed to wander around in that diaper, going when and where she felt like. I'd clean her up and then put her back into underwear.
We then gradually worked on SITTING on the potty (in the pull-up.) We wrapped up about 25 small presents (playdoh, markers, little toys, etc) and every time she went sitting on the potty with the pull-up, she got to pick out a package. She knew that when the presents ran out, it was time to go without the pull-up. She really wanted a "real" camera, so we said she could get one the day she pooped in the potty. When that day came, she was very upset and cried and didn't want to, but I really pushed her and stuck to my guns. After she did it ONE time, that was it. We bought the camera and never had another problem.
I've also heard of people using this tactic and then cutting holes in the pull-ups, so they'd wear it and sit on the potty and end up going IN the potty, "wow, honey, look at that! what a surprise!"
Sorry to say, this went on for nearly 8 months after she was potty-trained! But once she finally did it, she never had an accident and never had a problem after that. I kind of wish that I got tougher, sooner. But then, it wasn't worth having her get horribly constipated and in pain. And really, once I got over MY anger and frustration over the whole thing, I realized that she only pooped once a day, never had an accident and was in underwear the rest of the time, so it wasn't such a big deal to do this one diaper change a day. I have known and heard of lots of kids with this pooping issue!