To refuse to have faith implies a wilful refusal to do something one is quite capable of doing, but unwilling. But faith or trust are not subject to one’s will.
We can decide to accept as truth what someone says, or we can decide to not accept it. Faith has nothing to do with that decision.
We might accept it because we trust the person, or reject it because we don’t trust the person. That is faith in a human being, not God.
Some of us don’t trust the preacher or the Bible. We want to know if there is something behind the word that is being pushed at us. We need to know because the word sounds very unrealistic, based on what we do know.
We seek for some evidence, some sign, that there is something behind the word. But we find nothing. There is nothing to have faith in, whether or not we want to.
Refusal of faith is ridiculous; there is no such thing.