More is motivated by integrity. He will not bow to those in power when he believes the leadership to be less than laudable.
More feels that the Pope is corrupt and to comply with his edicts is morally unjustifiable. More explains, "What matters is not that it's true, but that I believe it; or no, not that I believe it, but that I believe it." More fears that if he breaks with his conscience, he will be damned to hell, while his associates and friends are more concerned with holding onto their own temporal power.
As for the specific objections to the Acts of Supremecy, More argues with Norfolk, his good friend who has bowed to the pressure of signing the Acts which he does not truly believe in:
Norfolk: Look, I'm not a scholar, and frankly I don't know whether the marriage was lawful or not — but Thomas, look at these names! You know these men! Can't you do as I did and come along with us for fellowship?
More: And when we stand before God, and you are sent to Heaven for doing according to your conscience, and I am sent to hell for not doing according to mine, will you come along with me — for fellowship?"