When it comes to finding antonyms for the phrase "seeking the hand of," there might be several words that could fit the bill. Some of the antonyms for this phrase could be "avoiding," "ignoring," "eschewing," "rejecting,", "disregarding," and "neglecting." These words could mean that someone is not interested in or actively avoiding the idea of being in a romantic relationship with someone. However, it's important to note that antonyms are not always absolute and could depend on the context in which they're used. Overall, the idea of "seeking the hand of" someone would have a different set of antonyms depending on the situation and the intentions of the people involved.