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After you give your reasons, your mother might have a response.  Do not interrupt her.  Try to make eye contact and nod, to show that you are listening. Take note of what she says, so that you can respond to it.  You want to be able to convince her, not argue with her. If you have listened carefully to what she said to you, you should have a couple things to respond to.  If she thinks that you are too young, you can respond by saying,”Everyone starts shaving at different ages.  This decision should be based on my maturity level.” Try to emphasize the fact that you are the one making this decision.  If you are submitting to peer pressure, or only want to shave your legs because people tell you that you should, shaving may not be a good idea. Your mother may just want you to ease into shaving.  Be willing to meet her halfway.  Compromises might be shaving below the knee, using hair removal cream, or having her help you shave. Suggesting compromises might be a good way to convince her. You can say, “What if we think of a compromise that can work for both of us?” Your mother may say no the first time around.  Wait before asking her again.  After about a month or so, you can suggest a compromise again.  Remind her that you were mature about her rejection of your request last time. It may take more than one or two tries to get her to say yes.  Stay mature and calm, and eventually she will agree that you are ready.
Hear her out. Calmly give your response. Be willing to compromise. Be patient.