What are some pointers and advice on how to stay neutral with arguementative people?

Firstly, don't get involved in the argument, right or wrong. It takes two people to argue so if you don't say anything and avoid eye contact then neither of you have won and neither of you have lost. In fact you've had a moral win because the person who picks the argument can't get satisfaction. They are fuming while you are still cool headed.

Hi...

Apparently, your mother in law is a defensive person and likes to cause conflict. I think the best way to handle it when she's trying her best to be annoying is to first smile..... the worst thing you can do is to react negatively or with defense in return, as this gives her fuel to continue her behavior.

You can tell her you're sorry she's upset or that she feels that way, and end it there. Sometimes saying nothing, wile LOOKING pleasant is a good idea... you're going to have to guage the situation. Be pleasant even if she's not. You can excuse youreself and go to the bathroom or just go home if you want to get away from the behavior.

If you continually work at being pleasant even when mother in law is not, she will eventually stop this type of behavior with you because she will finally decide it doesn't cause you to react or respond negatively. She wants to stir up some shlt, for whatever reason.

Some people don't appreciate things the way you do, so you can't expect everyone to be gracious if you've done something nice for them. Unfortunately, not everyone appreciates our efforts.

Don't try to understand it; you'll just make your head hurt.

When it's something truly stupid and petty, just nod and let them say what they want to say. Don't "feed the troll" by trying to contradict them or argue the point. Most of the time, they just want to complain for the sake of complaining, and the rest of the time they really WANT to pick a fight but if you won't engage then it throws them off balance when they basically wind up talking to themselves.

some people just don't know how to say thank you. it is frustrating for them so they start an argument so you will walk away and she won't have to embarrass herself trying to say thank you. just accept this and assume the thanks is extended. she will appreciate it and you won't feel regret.