It's not the same in most cases.
I don't think most men are targeting single mothers with the intent to physically abuse their children.
What happens is single adult men who are not in work and/or cannot afford to privately rent are last on the list for any kind of social housing. Even if they are care leavers or addicts or suffering from mental illness, there are still lots of families, disabled people, refugees and single Mums with children who are ahead of them.
Their choices are sofa-surfing with family or friends, street homelessness or hostels if they can get one. All shit.
Or they meet a woman willing to enter into a relationship with them and invite them to live with her. Who usually has children.
And the men are often dysfunctional, as are the women. And the drug use that usually is part of these relationships and the abuse which is usually part of these relationships occurs. And you have women who just want a man in their lives for whatever reason and a man who might not even like the woman so much but she's providing the roof over his head and it's preferable to sleeping in the streets or in a hostel.
Or he might like her but it's not his kid he's suddenly playing step-Dad that he has no bond to and it's likely the child is annoying to him crying or needing attention or they can't do the things he wants to do as a couple because there's a child to consider.
So he feels trapped. He could leave but the alternatives are shitter than the way he's living now. So he gets more and more resentful and abusive.
It's not in any way an excuse. He could always choose to sofa-surf or be street homeless or live in a hostel. And he could choose to not be an abuser. But the women could also choose to not move in someone quickly and ignore or facilitate the abuse of their children.
It's just what happens in a lot of cases.