The phrase "gave eyeteeth for" expresses extreme desire or willingness to sacrifice something valuable for the sake of a coveted item or experience. Antonyms for this phrase can include "uninterested," "indifferent," "apathetic," or "disinterested," indicating a lack of strong desire or willingness to make significant sacrifices. Other antonyms might include "content," "satisfied," or "fulfilled," suggesting that the individual does not feel any pressing need for the object or experience in question. Alternatively, "prudent," "cautious," or "risk-averse" may be used to imply that the individual is not willing to risk important assets or take on major risks in their pursuit of the desired item or experience.