No. I'm saying that the OP may have omitted important details, so that the portrayal of the situation is skewed.
I'm saying that maybe there were difficulties with the child, maybe slowly, over time, over years, the mother has reached her wits' end, maybe she cries to herself about how things have gotten out of control and how she can't cope. Maybe she shouts at OP rather than at the child, as people have assumed, because maybe OP is a parent who is soft and undermines his wife when it comes to the children and their discipline, and maybe that has slowly caused problems with the child. Maybe one or two added details or omitted details have turned OP's reality of "my wife can't cope and I'm not exactly helping" into a story for us, for effect, of "oh and did I mention she doesn't feed the kid sometimes".
Somebody will say that it's a lot of "maybe"s. Yes, because I don't know them. I'm as unsure of the situation as you lot who are also making your own assumptions based on the limited information OP has given us.
I'm sure we all know people who have a child they just keep having problems with, and as far as we know the parent is doing all they can but they simply cannot get things under control. For all we know, it could be that kind of situation, which is what I meant when I said maybe the lying and stealing came first. Okay, these behaviours will be driven by something going on at home, but not necessarily the abusive mother OP has told us about.