Short answer: sexism.
Long answer: Doctors will often refuse to sterilize DFAB people, and insurance companies will refuse to pay for sterilizations, unless we’re literally dying, because they assume we’ll always regret it because we’ll always want more children by the simple fact we’re “women” and as such our only instinctual drive in life is to be mothers.
And this DOES include denying trans people transitioning needs and procedures.
Even people who’ve had children have had to fight to be sterilized - my aunt, for example, had a serious disease in her uterus, which was putting her in so much pain she could barely leave bed, but they refused to remove her uterus until they had made her pay an exorbitant amount to “exhaust all options”.
As your mother has pointed out, some doctors/insurance policies will allow DFAB of certain ages to go through sterilizing procedures, including tubal ligation. The earliest I’ve ever heard is late 20s, but some may not serve you until your 40s or even 50s. However, I don’t know what one has to do in order to be given this chance, as I’m waiting to begin trying myself. All I know is that it’s almost always a struggle even in these cases.