So is battering just a psychological problem?
No. The ultimate answer to why does he batter is: BECAUSE HE CAN. What that means is that the society has given him the idea that a woman is property, his home his castle. Behavior he knows he'd never get away with in the outside world, seems to be permitted at home.
(Some batterers are also aggressive outside the home - this is not a good sign but at least it makes this type of man more predictable. The inconsistency of many batterers' behavior at home vs. outside is more confusing for us to grasp.)
So we're saying that not all men are batterers, it takes special circumstances to motivate abusive personalities - but once formed, these men who might like to abuse many people get the message that there will be consequences for so doing everywhere EXCEPT with his woman. That's what is meant by he does it BECAUSE HE CAN.
Another way to put this is to say that it takes a combination of culture and family dysfunction to create an abusive personality.