What do you call it when someone agrees just to avoid an argument?

If you're looking for a single word rather than an idiom, I think placate works well.

From Merriam Webster:

Placate

Transitive verb

: to soothe or mollify especially by concessions : appease

They are probably playing along (with you) just to avoid an argument.

TFD(idioms):

play along (with somebody/something)
to seem to support or be friendly to someone or something

He knew that if he didn't play along with the reporters, they would write unpleasant stories about him.
I don't really like their idea that much but for now, it is probably a good idea simply to play along.

Cambridge Dictionary of American Idioms Copyright © Cambridge University Press 2003. Reproduced with permission.

B is humoring A.

From Merriam-Webster:

² humor verb

transitive verb

1 : to soothe or content (someone) by indulgence : to comply with the temperment or inclinations of • The only way to get along with him is to humor him. • I know you don't agree, but just humor me.

They're going with the flow -

To do what other people are doing or to agree with other people because it is the easiest thing to do

I wasn't very keen on the decision but it was easier just to go with the flow.