Antonyms for the phrase "availed oneself of" might include "ignored," "overlooked," or "rejected." These words suggest a lack of action or choice when it comes to taking advantage of a particular opportunity or resource. Other potential antonyms could include "abstained from," "surrendered," or "forfeited," each implying a deliberate decision not to participate in a certain activity or to give up an advantage that one could have pursued. Ultimately, the choice to avail oneself of something can have significant consequences, and different words can help to emphasize the importance of that choice in different contexts.