I really don't understand your mentality (Unless you're just playing devil's advocate).
"why should we care about sexual abuse of females" or anything else that doesn't touch us directly - I like to think we're not a race of sociopaths/psychopaths, that a lot of us have empathy and compassion on some level and some of us want to make the world a better place.
You might as well say, why should we care about genocide or famine if it doesn't affect us?
I think a lot more injustice is caused by horrific things happening and no one doing anything, or people taking action way too late, versus your argument, that a lot of injustice stems from action actually being taken. You would really use an example something as mundane as destruction of property over some short-term protests? And I bet that much more positive change will come out of the protests than whatever damage is being done. If nothing else, the officers responsible actually got arrested.
"And a lot of destruction is caused too..." - how about the destruction that is caused when a child is forcibly raped for example? So long as we don't know them it doesn't matter and no one should "interfere?" And what about when things like sexual or physical abuse aren't "handled within the family" and nothing happens at all, and the child just needs to deal with it for years on end? How about situations where "breaking the family apart" - I assume that means the perpetrator actually getting arrested and going to jail - ends the abuse and improves the life of the child?
Again I don't know if you're just playing devil's advocate, if not, I don't understand you at all, on top of which your argumentation is horrible.