There is no age limit on knife purchasing in California state law. Not only have I checked the California penal code, but I've lived in California for 45 years now, and I legally purchased several knives in stores here as a minor.
As for the OP, you're 15 years old, and your mom is YOUR MOM, that means you aren't likely going to change her mind, or convince her that you are right and she is wrong, especially when the subject is knives and she thinks knives are weapons. Don't expect her to speak with you or listen to you as though you were her equal. Most parents (like myself) do not consider their children to be on an equal level. That's what it means to be a parent- we make an enforce OUR rules, whether our children think they are fair or not. I'm not saying to give up, maybe you can reason with her. Good luck with that.
The following is not meant as advice, but one of the most important lessons I learned as a child was how to keep secrets from my mom. Like every time my dad, or uncle, or grandfather let me do or have something cool and said "Now don't let your mother know". Such a skill (hiding things from my mom) also came in handy when it came to weapons and porn.
I consider myself fortunate that my mother didn't have a problem with me having knives (she and my father bought me a Buck 110 when I was 13), she only prohibited me from having knives that she thought
looked like weapons (which defies reason, but that's the way moms are sometimes). Of course her prohibitions didn't stop me.
Look on the bright side Schakalicious, in less than three years you'll be 18. So get a good part time job, study hard in school, and save your money. That way, when/if you go to college, and/or save enough money, you can move out of
her house and own and carry all the knives you want.
Sometimes it sucks to be a kid, but that's life. Being an adult sucks sometimes too

.