No I don’t think they do it on purpose at that age nor is it a matter of naughty behaviour ! Many children have actually a fear of letting go of their poo.
With holding poo can have to do with constipation in which case you should look at water and fiber intake.
Another cause can be stress. Stress is the most common reason for regression. Kids can be stressed by a new daycare, moving to a new town, an extended family member’s moving in, a parent’s illness — anything new or different.
Another factor is that children at that age are often very active, they have no time to sit and wait for the poo to come (pee is/comes easier) or simply get distracted. The thing with poo is you can get an urge to go but when you don’t act on it the urge goes away at least for a while. The longer you wait the dryer your poo gets and then it may cause pain and fear to pass. Some kids find it also scary that a product of their body is flushed away , what if they flush away themselves ? Often that sense isn’t there with a pee since a pee is liquid and not solid like a poo.
Be calm understanding and patient. It will come in their time. The more pressure you put on it the harder it becomes. I would also suggest never to label poo as dirty or yuk or never to comment negatively on a poo on the pants.

There are really interesting comments on this!

It sounds a bit like Encopresis, she may not be being naughty but in fact has lost control of her bowel function.

My daughter did the same thing and we worked out that it was because my son was just born and she was looking for some attention – in directly.

Find something else to take away from her a toy or make her sit in a cnr for 4 mins.

Usually when young children regress it is due to a stresser….such as changes in her routine or life in general….has she started preschool or school? Many small events are actually huge events for young children. I would also seek advice of the GP and go from there, if problem persists a paediatrician may help to find out the underlining issue, all the best!

Hope this was just a phase for you.

Time for a visit to the doctor I think.

I hope that its sorted now

At age two they understand they have Done a poo in their nappy . . Age 4 is misbehaving I think.

Hope you managed to get it sorted out. My girl went through a stage when she was 3, where she would hide in her room or under the table to poo, I just kept telling her every time that she needs to do it in the toilet, and she eventually got there. Sometimes things can take a bit of time, but if you’re worried get her checked

I would get her checked out and I don’t think at any stage punishment and toilet training should be combined

Does she feel embarrassed by it at all?

You probably need to make sure that she does in fact have control or not. It might be worth checking out as some problems can cause this.

It could very possibly be an attention thing? Try a rewards chart?

Get her checked out may be constipated (other poo can come out round blockage) or have urgency issues

It sounds like she is probably doing it for a lttle attention. I wouldn’t punish her for it, but would let her know it is wrong and maybe not give her treats until she will use the toilet

if you are really stress you could get her checked out at the doctors or maternal health nurse

it could be a phase or he might not know

I would worm her if she has access to pets as this could cause her problems, she may be itchy and cant tell the difference at the moment.