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To understand the terms trans woman and trans man think about what the person would want to be, their biological sex is the opposite of that. It wouldn't make sense for a biological male who wants to be a woman to call themselves a "trans man" because they don't want to be a man, they want to be a woman . If a biological male who wants to be a woman were to call themselves a "trans man" then they would be reinforcing the idea that their gender is synonymous with their sex, which is against what they believe.
I like the term ftm and mtf are a lot less confusing.