If you’re not certain you’re right, don’t argue. You might debate, but don’t argue unless you are certain winning is possible and you intend to be the winner.
Don’t get sidetracked. Keep the argument focused narrowly on the point you intend to take.
“Molesting a child under the age of 13 is wrong.”
“But what if the sex was consensual?”
“Molesting a child under the age of 13 is wrong.”
But what if the other kid is only 16?”
“Molesting a child under the age of 13 is wrong.”
Etc.
Do not curse. It gives the other party a legitimate reason to derail your argument and put you on the defensive. Ground given up needlessly.
If the argument is in person, never raise your voice above “loud”. No shouting or screaming. If it’s on the phone, I find it effective to gradually raise my voice as the conversation continues. It’s effective because if they don’t give in, you’ll be transferred to a supervisor or ‘bad apple’ specialist who will have more leeway to and incentive to get you off the phone.
Be polite, and if the other party is not polite, call them out on it. “I listened to you very politely and I do not appreciate you trying to talk over my response.”
Remain calm and pay attention. People do not expect other people to pay attention any more, and there’s nothing better than using the words a person said 5 minutes ago against their current argument.
If you’re on the phone and getting completely stonewalled, let her rip! The rules are off…scream yell and curse. You’ll feel better when you get that supervisor, and can now start all over with the sweetness and light routine.
I could write a book on getting your way. Friends who have witnessed my end of an argument with a phone rep usually say “YOU call!” the next time something comes up.