The phrase "seek the hand of" typically refers to asking for someone's hand in marriage or a serious commitment. Some antonyms for this phrase could include "reject," "decline," "refuse," or "withdraw." These words convey a sense of distancing oneself from the idea of a serious commitment, or choosing to not engage in a romantic relationship. Other antonyms that are more neutral could include "ignore," "disregard," or "overlook," which simply suggest not actively pursuing a romantic relationship without necessarily rejecting it. While seeking the hand of someone can be a meaningful expression of love and commitment, there are certainly valid reasons for choosing to avoid such a commitment.