This^ Plus he was struggling against the power. He was afraid that he would turn into a monster like Peter, so i'm assuming that he didn't fully accept the role of an alpha until the end of season 4.If you see the last episode of the finale season you can see that in the end of that epsiode he finaly caught what is the meaning of a trua alpha and then he defeated Peter easily. I think he didnt know how he can used his new powers
He isn't just a beta. He and Derek evolved into something greater because Derek defeated a beserker like it was nothing. I think it's because they were born as werewolves.peter is still a beta and i dont think defeating him is a big step up