This idiom or expression has to do with:

Fighting.
Beginning to heatedly disagree.
Starting to hotly argue over something.

We were about to come to blows when he suddenly apologized.

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 like sentence means:

They were all fighting.
Fighting was going on.

This idiom or expression means:

Getting ready to fight.
Situation getting worse.
Expecting fighting to begin.

Q. It’s a nasty campaign. Do you think gloves will be coming off?
A. As far as I’m concerned, the gloves are off already!

This idiom or expression means:

A slight chance.
A chance to win, but with difficulty.

A. Are you gonna try for the team?
B. No, I don’t have a fighting chance.
A. Then I won’t either.
B. No, you should. You can still do it, but you really have to work at it.

This is about asking or wanting to fight.

If someone says: Do you want to step outside? it usually means:

Let’s step outside because I want to beat you up.

Also:
Taking it outside.
Continuing it outside.