If you want a phone, you should try to give your parents several reason why you need a phone. Make sure your reason aren't immature and unimportant (ex: talk to friends, social media, etc). Instead, give reasons such as texting a family member you see rarely or to contact parents at school incase of emergency.
You could also find a way to earn a phone. You could do extra chores for pay and buy your own phone. If you do buy your own phone, you'll probably have to pay your own bill.
Another thing to bring up in your argument is what you would do if you had a phone. Explain how you would care for it, and set curfews. If your parents talk about making a rule such as no phone on Sundays, you should not argue with this rule until you actually have the phone, or at least try to compromise with them.
You could also convince them to get you a phone by asking what you would need to do to earn it. Maybe you need to get all A's or walk the dog. If they don't give you something to do, you could still find a way to impress them, without them asking. If you suddenly start showing more responsibility and maturity, they will most likely start considering a phone.
Hope this helped!
-GymnastPower (Girl's Advice Column)