"Throw in with" is a phrasal verb that means to join or side with someone or a group. Some antonyms for this phrasal verb could be "oppose," "resist," "refuse," "deny," or "disagree." Opposing or resisting an idea or decision means to take a different stance from the person or group. Refusing or denying means to decline an offer or proposal. Disagreeing means to have a different opinion or to disagree with someone's stance on a particular issue. These antonyms for "throw in with" create a balanced negotiation in which both parties have the freedom to express their beliefs and concerns.