It is interesting you bring this passage up. I'd been struck by it rather profoundly yesterday prior to posting this topic, and it was part of it even though I didn't expressly quote from it. I'll share briefly my thoughts and how it relates to this.
As we differentiate ourselves from other we naturally create boundaries of what pertains to or defines us, and what does not. In our group formations it is the same thing on a collective basis; what belongs and what does not; what or who is in, and what or who is not. This is not necessarily in itself a bad thing. However in order to emphasize and stress these divisions we demonize the "other" that we cannot reconcile with those things our group values. We make them the "enemy" of us.
Now the very exact same thing is what we do to ourselves as individuals. We split ourselves off from ourselves, we deny, reject, repress, and even hate those parts of ourselves which do not fit that image of what we wish we to see ourselves as. Much of that image is one which our culture tells us is good, as well as bad. The first "enemy" we encounter is the enemy within us. But that enemy is not an overt foe we can say "I hate you" to openly, as it sits in the dark of our own psyches, which in the dark corners of our minds we imagine as growling at us like an angry dog we keep locked in a cage in a dark room in our house wishing it did not exist, denying it exists and is at the end in fact us.
So to "love your enemies" is first realized in ourselves, with ourselves. All has to be brought into the Light. "For there is nothing hidden that will not be disclosed, and nothing concealed that will not be known or brought out into the open." When we learn to "love your enemies", you first learn to love yourself. You don't vanquish and destroy these demons, this "evil other", but rather you see beyond the eyes of hate, with the eyes of love through Love.
At which point, that which was your enemy is seen as a creation of your own demon-making process, and Love dissolves that relationship and allows it to become an ally in service of our greater good, not working against us, but for us. It's hard to explain this, but imagine how a child only wants your love, and acts out badly when it feels mistreated and rejected. To "overcome" the bad behavior, it is often better done by getting rid of the source of it. It is better to love, than to hate.
"Do not fight to expel the darkness from the chamber of your soul. Open a tiny aperture for light to enter, and the darkness will disappear." ~St. Porphyrios. Love truly overcomes, and this is how it does; not by force, but by Grace. Love your enemies applies to all our relationships, especially our own selves first. As we learn how to love our enemies beginning first with ourselves, then we can love the whole world.