The phrase "eating one's words" refers to the act of retracting something one has said, particularly with humble regret. As such, the antonyms for this phrase would be words like "sticking to one's guns," "standing by one's statement," "maintaining one's position," or "refusing to retract." These are all opposing phrases that suggest a strong conviction and refusal to back down from a statement, as opposed to the regretful act of retracting one's words. While there are a variety of situations where retracting a statement may be necessary or appropriate, these antonyms suggest an opposite mindset of resolute and unwavering conviction.