The phrase "give over to" means to devote or surrender oneself to something or someone. The antonyms for this phrase are terms like resist, oppose, protest, or stand against. When we resist something, we refuse to give in to it and work against it. When we oppose something, we express our disagreement or disapproval of it. To protest is to publicly express an objection or disagreement with something. The phrase "stand against" means to resist or block something. Therefore, if we do not give over to something, we would be resisting, opposing, protesting, or standing against it. Ultimately, the antonyms for "give over to" suggest a willingness to challenge, question or reject something that we feel is not beneficial.