Either I do something terribly wrong or they are simply not my true friends.
Those are bad friends.
people like doormats cause they can control them
It's often because your friends don't have the same points as you.
It could possibly be your method. I have a friend who, when he's standing up for himself, is too aggressive, even though he doesn't think so. It irritates people, and pushes them away because it turns him into "a sensitive jerk".
I stand up for myself, but I always be sure that I'm firm, not aggressive, and make it clear that a doormat is not the way I am from the start.
It is possible you just pick bad friends too. -shrugs-
I had that same problem XD it can be hard to identify who will be a good friend. I've always been very selective about friends, sometimes it means I'm the loner but the friendships I form are deep, with great similar interests and long lasting. I just found other people who couldn't stand the things that I couldn't. So it's worth it.