THAT is a very good question PaulyWally. It all comes down to gender.
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Definition of gender in English:
noun
The state of being male or female (typically used with reference to social and cultural differences rather than biological ones)
Usage:
The word gender has been used since the 14th century as a grammatical term, referring to classes of noun designated as masculine, feminine, or neuter in some languages. The sense ‘the state of being male or female’ has also been used since the 14th century, but this did not become common until the mid 20th century. Although the words gender and sex both have the sense ‘the state of being male or female,’ they are typically used in slightly different ways: sex tends to refer to biological differences, while gender refers to cultural or social ones.
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You guys seem to be stuck on the biology so let's look at that.
Yes, with genetic gender, genetic males normally have an X and a Y chromosome (XY), and genetic females normally have two X chromosomes (XX).
There is also a condition know as klinefelter syndrome where you get (xxy) chromosomes or (xyy) or (xxx) or (xyx) or (xxyy) or (xxxy).
Chromosomal configuration is not the best for determining gender, but do use the same "sex" terms (Male/Female)
Now the social and cultural discussion.
A persons gender is determined by gender identity. Gender identity is a person's private sense and subjective experience of their own gender. This is generally described as one's private sense of being a man or a woman, consisting primarily of the acceptance of membership into a category of people: male or female.
NOW, to answer your question "How can you "no longer" be a man?" By changing his gender identity (as well as his body), Bruce stopped being the gender male and she started being the gender female. SHE did not change HER chromosomal configuration, but just her social and cultural differences that make her gender.
Lastly, if you have wings grafted to your back, it doesn't make me a genetic butterfly... but it might make you social butterfly. (ba dum tsh!)