because we arent talking about adults, we are talking about children, YOUNG children and in this case the boy is possibly only 3, his behaviour has taken place in the last school year where he was 2-3yrs old, he is learning! and as horrible as it is our children do have to learn to deal with stuff like this.
the pre-school should have dealt with it if its as bad as the op says, that is the problem, not the child. and no i dont think a 3 possibly 4 yr old should be labelled as a bully.
the idea that at 3/4 yrs old a child is deberately choosing to pick on one child and repeatedly being mean to them out of malice doesnt sit with me.
he may be snatching from her because she likes the same toys so therefore it is always her that has the toy he wants. they tend to lash out and push at those closest to them (vicininity wise) again this could be because they have similar interests, or just bad luck that she is always the child next to him. his behaviour needs addressing but no i wouldnt say it is bullying. at this age they are still learning to understand their feelings and have some assemblance of control over them. they are learning to share and take turns, some find this easier than others.
and i would be very suprised by a teacher that agreed a four year old could be a knowing bully. my dp and all the professionals he works with (in cp) so child psychologists and a variety of professionals would certainly disagree.
you may have a 4 yr old who hasnt been taught that this behaviour is wrong, or shown how to share and to control and manage his emotions and behaviour, in which case it is the parents/caregivers responsiblitly to teach the child who wont even know what htey are doing is wrong if they are not told it is.