Giving over to is a phrase that implies surrendering or submitting to something or someone. The opposite of giving over to is resisting or opposing. If someone resists, they refuse to give in or comply with an opposing force, while opposing means to go against or contradict something. Another antonym could be retaining, which means to keep or hold onto something rather than giving it up. Also, the word veto could be used to describe a more active opposition to something, where one has the power to strike down or prevent an action from happening. Overall, giving over to has several antonyms, including resisting, opposing, retaining, and vetoing.