To expand on what Kenshi said, Vegeta was born in a planet in which strength means everything. And being the prince of Saiyans, and stronger than the King since he was a kid, means he believed he was entitled to be the strongest Saiyan there was. Being outpaced by not only someone he considered to be a low class warrior, but also the very same low class warrior who forced him to use Oozaru back then, in getting the very form he has desired in this entire arc, has done a lot to hurt his pride and self-esteem. Add to that another Super Saiyan who comes out of nowhere, and yeah. Someone like Vegeta suddenly feeling the need to prove himself to everyone and set "right" what was set wrong in the pecking order certainly makes sense.
However, there is no excuse for this part of his characterization getting past his "You Are Number One" speech from Boo arc.