Learn to identify when someone is looking for an argument, and don´t fight them back on it. Something I´ve learned is that when someone is looking for an argument, you will never win. And even if you defeat the basis of their argument, they´ll come back at you with something else, because they just want to argue. They are unliely to be open to seeing anything through yor eyes, so step back and don´t give them your time. Respect their view on the basis that, no matter how wrong they seem (or are), they are entitled to their opinion and you can´t stop them having one. Explain to them that you are both entitled to your own opinion and you´ll agree to disagree, and leave it at that. Regardless of how much they antagonise you.
I understand that you are likely to be desperate to make them see a better way, but let it go. Arguing with them will only have an impact on you and your mental well-being, because you are the one that will suffer through the arguing- they´re probably enjoying it. Don´t take the bait, step away and forget about it.
I have deduced that there are two kinds of arguments. The first kind of argument is the one where the other person is hell-bent on arguing and have no interest of a fair argument, but have other insecurities or motives layered below their argument, which mean that for you, it´s not one worth fighting. The other is the kind where two people hold two different sets of beliefs and have a genuine interest in sharing those and trying to make others open up a little more to their way of thinking. Depending on the open-mindedness of yourself and the other individual, you´ll hopefully meet some form of compromise in this kind of argument.
Finally, I don´t really believe in ´arguing´. Debating is better than arguing (for me, debating is clearly articulating your opinions on a matter, where as arguing is allowing your emotions and other factors colour your debate, which isn´t the dictionary definition at all, but I think is the way we consider it to be in contemporary culture.) Debate is good and healthy, it´s how we begin to make sense of our world. Keep your debates articulate, you are entitled to hold whatever opinions you wish to hold, and no-one is allowed to take that away from you. Debate well little girl, there´s a lot out there to talk about! Do it.
Arguing with Uncle Dan