> Some cultures still eat dog - you don't think they can love their children?
This is a non-sequitur.
edit: Compassion for one's in-group can be very real, even if the in-group is small. It's almost like a breadth-vs-depth question. I've even heard of some studies suggesting that having very intense feelings of compassion for one's in-group is predictive of callousness towards the out-group.
Sociopaths score low in empathy but are excellent at perceiving others' emotions.
"Hate the sin, not the sinner."
The WWI Christmas truce in 1914 shows this dynamic very clearly. It’s likely these people had great empathy for each other as they where in similar situations even sleeping in the same trenches as the front moved around. Yet, eventually they went back to killing each other. https://en.m.wikipedia.org/wiki/Christmas_truce
Wishing others harm and being able to empathize are tangential concepts.
The ability to understand what it's like to have something terrible happen to you does not preclude you from wishing it upon your enemies.
I suspect that for a subset of people the ability to empathize with people who are suffering makes the suffering of their enemies all the better.