He wanted a divorce and didn't like having Catholic authority higher than him.
He blamed his wife for not giving him a son to be his heir, so he wanted to divorce her. Catholics do not allow for divorce, so if he was going to marry another woman and have a legitimate heir, he had to break away from Rome to make divorce allowed.
Henry wanted more power for himself and England. He, like the other kings of his day, were under the authority of Rome. They, in essence, had to comply with the commands of Rome or they faced severe problems. He didn't want to be ruled from Rome, so he took this as an opportunity to kill two birds with one stone.