Feelings come and go all the time and can make you believe in them being real. Well, in Mindfulness therapies and related we learn to observe feelings; you have feelings but they don't say much of who you are. Or anything about others for that matter.
This is especially true when we come to feelings of sympathy and antipathy. To put it in the frame of psychological language, sympathy is when you have positive feelings for others. Which are often based on seeing qualities you like in yourself. Sometimes there can even be an admiration for someone’s characteristics; traits you still haven’t developed yourself. Antipathy is obviously its contrary. Projected feelings of those negative qualities we don't see or know of, but dislike in ourselves.
People who are used to work upon themselves and have some insight in their own psychology, will have heard of this. What's interesting is when we look beyond the feelings of sympathy/antipathy and try to change how we see the other person. Since ourselves are the only persons we can change.
The brain finds it hard to change the way it sees things or people and will likely not change its opinion of someone. Unless we become aware, which is the first step.
One experiment to try out next time someone really annoys you, could be to focus on the other person’s most positive features. It can happen in the actual meeting or when you have stepped away from the immediate situation and look back on what happened. It might be something small or something you've seen rarely.
Your way of shifting focus does something almost magical to the relationship and the person will start showing new sides. New ways of seeing each other will open up for a new understanding. It may take some time apparently. As mentioned... the brain doesn't like to change what it already has set on.
Also, you can't see more than you've seen in yourself. And the same kind of empathy you have for yourself is the way you empathise wth others. Still - it is worth trying out new ways than staying inside the same old box, isn't it?