It is not "trustworthy". But I don't have a criticism of it. I don't reject ideas for no reason.

Um, there's a lot of criticism out there of deductive logic. For one thing, humans often make mistakes in deductive logic so one doesn't know if something is correct. For another, some philosophers have rejected the law of the excluded middle. Yet others have proposed logical systems which try to localize contradictions and prevent explosions (under the sensible argument that when a person is presented with two contradictory logical arguments that look valid to them they don't immediately decide that the moon is made of green cheese). There's a lot to criticize about deductive logic.