Antonyms for the phrase "hath no taste for" could include "has a strong passion for," "is eager for," or "desires greatly." These words convey the opposite meaning of lacking interest or enthusiasm for something. Other antonyms could be "craves," "yearns for," or "hungers after," suggesting a strong desire for a particular thing or experience. Conversely, "dislikes," "hates," or "avoids" could also be antonyms, indicating a deep-seated aversion to something. Overall, these antonyms help to provide a range of different ways of expressing emotions and preferences, allowing for more nuanced and varied communication.