Because Rinko's answer to that is neither yes or no. She didn't think of who she's really doing it for, and what kind of future she will have with either choice.
FearlessDawg's reply points it out. Rinko is desperate.
When she turns into a male all the sudden without ever wanting it, her world falls apart. Right now, she only cling on to the hope that if she become a woman again, the feeling of certainty about her life will return. So it's not just she want to be a woman, she think she
need to be a woman.
And of course, when mom bluffed about doing it for a guy, she can't say no with certainty.
Other thing is as her mother said, she know what it is to be a woman before the change.
The gender change surgery will not be the same, and she will not get what she wanted: the feeling that this whole gender change syndrome is just a nightmare that will disappear like it never happened. She need to realise that, and think again if she can accept that compromise.
If Rinko can answer yes with certainty, and accept the consequences, her mom would accept her choice.