Ummmm, no.
I never understood this at all.
If it makes sense can someone explain how and why?
It appears to make absolutely no sense whatsoever.
What does it mean and how and why does it make sense?
Love my enemies, gotta say nope on that one until someone explains it, that is if it makes any sense at all.
I reserve my love for a select few in my life and simply have no enemies.
I’m no theologian, but I’d guess it’s about letting go of hate and accepting the imperfection of man. Also, it might be about putting judgement and vengeance into the hands of your God.
“I have not come to bring peace but a sword” -something Jesus apparently said.
Listened to a sermon about this quote several weeks ago but I felt that it didn’t quite explain it but merely glossed it over.
I think this is a very interesting quote though as his ministry did indeed result in the sword far more so than it did peace for most of Christianity’s history and did indeed set family member against family member.
But then I’m not even a Christian so…
I think what the saying means is that love conquers hate. That the feeling of “love” will be stronger than the feeling of hate and it will disarm yuour enemies.
When you have hate and anger towards someone it’s like them renting space in your head. The Buddha said “anger is like drinking poison expecting the other person to die.” It hurts you more when you hate someone. It’s better to love and forgive those who have hurt you, then to hold a grudge. 
Perhaps he was stating that to everyone at once.
Maybe it went for everyone, not just one guy getting literally beaten.
I think it’s eye for an eye, but that doesn’t need to be a bad thing.
The only way love your enemies makes sense is if it goes for us all at once, i don’t think it mean literally do good things for someone hurting you or love someone who harms you, i think it means for everyone to not harm eachother, but it has to be eachother, not just one person getting literally beaten.
Eye for an eye.
I don’t think you have to love your enemies, just do not allow the hate consume you
I think it’s to see them as human beings.