The phrase may imply gender stereotypes, particularly in the example referring to a man's heart and food. Remember, the way to a man's heart isn't always through his stomach; interests vary.
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Figurative Meaning
It's a metaphor for what makes someone happy or emotionally satisfied, not a physical path. She discovered the way to her teacher's heart was through diligent study and original ideas.
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Variability
The phrase can be tailored; replace 'heart' with what best fits the individual's passion or interest. For the avid reader, the way to their heart is through a good book.