Yes, I've felt this way before. But not about family members - though we have butted heads from time to time, I try to keep in mind that at the end of the day we are on the same team.
Who I have felt this about, is people that have tried to bully me or push me around. Part of it is the offensiveness of it, like they have the audacity to pick on me, like I look like someone weak to them, that they think they can screw with. It makes me want to get mean, myself. The fact that they saw me as a target, dared to pick on me, plus the fact that they have obvious weaknesses/flaws/shortcomings of their own, makes me even angrier. Like who are they, to screw with me. It makes me want to show them that they bit off more than they can chew.
Idk. The best thing for me is to try to forget. If I know I don't like someone, all I can do is just try not to interact with them as much as possible. After all, people like this want attention, because they're childish, they want to see that they ruined my mood because it makes them feel like they have power and control over me, so it's best not to give them what they want. And also, like I was saying, it helps me to remember that everyone who has picked on me, both in the physical or online worlds, have been very flawed people themselves. There's definitely something wrong with them, for them to act in that way, and the way they are is a reflection on them, not me. So that helps me to feel like I don't have to worry about what they said to me because it doesn't mean anything, coming from people who clearly have issues/frustrations/weaknesses themselves.