This idiom or expression has to do with:

Arguing.

Q. How do you feel about kids who keep talking back?
A. I don’t think they’re cute!!

Also:
Back talking.

This idiom or expression means:

Verbally fighting.
Arguing very angrily.

A. I thought they were going to kill each other.
B. I know, they were really going at each other’s throats!

Also similar:
Duking it out.
Going at each other.
Letting each other have it.

This idiom or expression has to do with:

Arguing.

He doesn’t want to take issue with her because he doesn’t like speaking or going against her.