I have encountered a claim that people love others for traits that they have themselves, and I have also encountered a claim that people hate others for traits in themselves that they reject. That is not always true.
People love others for traits that they value, and they hate others for traits that they dislike, whether or not they themselves have these traits.
There are many people who love Jesus Christ. That does not mean that they are all Jesus Christ. There are many people who love Gandhi and Mother Theresa. That does not mean that they are all Gandhi and Mother Theresa. There are many poor or powerless people who love any number of wealthy or influential people. There are many people who love kind and generous people whether or not they are themselves kind or generous.
We see the exact same thing with hatred. Just about everyone hates Hitler and Jeffrey Dahmer, but that does not mean that they are themselves Hitler or Jeffrey Dahmer. There are many people who are hard-working who hate people who are not hard-working. There are many people who are compassionate who hate people who are not compassionate. In none of these situations is hatred for the traits that one has oneself.
The women I've loved had some things in common with me and some things different from me. They were all, like me, interested in creative pursuits and philosophically minded. However they were also different from me in many ways. Michelle was kind, warm and compassionate when at that time in my life I was quite mean-spirited. Julia was joyful and optimistic when I am quite morose. Melanie was brave, strong-minded and good with people, which I am not. And of course all of them were beautiful, when I get both positive and negative comments on my appearance. I loved the traits that they had that I did not have as well as the traits that they had that I did.
With people whom I have hated, I had a few similarities to some but very few to others. I hated them for traits that I disliked, whether or not I had these traits. In most cases I didn't. I hated men who beat their wives and rape their children, because I do not like to see women beaten and children raped. I hated the Spanish colonialists for what they did to the Incas, the Moores and the Aztecs. I hated the people who burn the Amazonian rainforest because I do not like to see precious treasures destroyed. I hated the 1990s feminists because of their malice. And I hated the gangsters and the Russian mafia because of their cruelty and destructiveness. Of all these, probably the only ones with whom I have anything in common at all are the feminists – who, like me, were brainy people who had been unattractive in high school and did not like their place in society.
There is however a way in which the proponents of this concept appear to have a point. And that is: The more you focus on someone else - in love, hatred or anything else - the more you leave yourself open to influence by that person. As Nietzsche said, "As you gaze into the abyss, the abyss gazes back into you." Focus - not love or hatred - appears to create a bridge between you and the next person. The more you focus on Christ the more you become like Christ. The more you focus on Hitler the more you become like Hitler.
We see the latter with Ayn Rand. She fixated so much on Hitler and Stalin that she started to act like them. She was calling people "lice." She decided that anyone who had any disagreement with her philosophy, no matter how minor, was evil. Whereas to the extent that she focused on better people like Aristotle and Thomas Jefferson, she produced genuinely valuable thought.
I have seen this work out in my own life as well. For a long time I was focusing mainly on bad people, and I acquired all sorts of negative traits. Whereas now that I focus more on good people, more people are telling me that I am a good person.
So no, love and hatred are not about the traits that you have. They are about the traits that you value or not value. However the more you focus on what you love, the more you become like it, and the more you focus on what you hate, the more you become like it as well. The latter is a strong argument in favor of acquiring a better focus. The mechanism for this however is not love or hatred. The mechanism for this is focus.