I wish I could remember the story more clearly, but when Prince Siddhartha’s (the Buddha) father forbade him from leaving the palace grounds (which he wanted to do to experience for the first time the struggles and sufferings of the peasants and commoners), he sat outside his father’s door for days until his father realized his son’s conviction and aquiesced.
Confronting a parent on an issue such as this can be difficult for persons of any age. I’m sure many adults here will admit to backing down from a decision because of their parents’ influence. Having an emotionally charged argument about the subject often makes it even harder.
I’m not calling your mom a bully, but conducting an argument based more on emotion than reason is something of a bullying tactic. The way to defeat it is with truth (conviction), courage, and perserverance. Whether it’s calculated or just habit, your mom will be expecting you to give up by showing how upset she will be. And she may escalate that hysteria if at first you don’t back down. However, she can’t keep it up forever, and eventually on or both of you will realize that you’re not responsible for her perceptions and feelings (she is), especially when you believe you are doing the right thing for yourself, and she presents no convincing evidence to the contrary.
So, what you need to do is sit outside her door. Make a simple case and state it plainly. Let her react. Do not react against her. Instead repeat your argument word for word, and let her react. If she brings up legitimate concerns, address them and return to your argument. Repeat until she stops reacting and starts listening.
You’ll have to outlast the tirades and not get emotional, which you don’t have to if the truth is on your side. Good luck.