He didn't really. He disapproved of the genocide that was being committed on the Na'vi, and he couldn't let it continue. Jake saw the RDA and the personel as wrong. In his opinion, the Na'vi were doing nothing wrong, but defending themselves and their home. The RDA wanted what the Na'vi's Hometree was sitting on, and took it forcefully, to Jake's disapproval in his kind.
Also, what does race mean? Race is just a species, a body. But, all bodies have a soul. And there's no race for soul. All souls are the same. So, in a way, he didnt betray his own race.The Na'vi are his true race. Think about it.Eywa has chosen him.