I see a lot of posts here that speak about "holding frame" with respect to maintaining emotional state or composure. However, frame and state are different and complementary aspects of dealing with arguments and discussions.

A frame refers to Framing Effect which refers to a cognitive bias in psychology. Think of a mural on a wall that is so large, that its impossible to discuss it in entirety. So you choose to limit the area of discussion by placing a rectangle, framing a partial area of it as a picture. You can now speak about the contents of this rectangle pretending those are the only items of relevance.

Reframing occurs when another participant moves/resizes the rectangle, thus taking out things that give strength to your points and bring in things that give strength to their points. This is usually done when your argument is solid and instead of conceding, they simply reframe to their advantage. They will keep reframing every time you show strength and the discussion ends with either them winning or running out of time. Often reframing will change the nature of discussion and put you on the defensive, since you would be discussing things you did not expect.

Reframing is a classic female argument technology. You may as a man have noticed that on a rare occasion, you were the one to pick a fight because you thought you had a solid reason and she had obviously made a serious mistake. But five minutes later, you find yourself apologizing to her and wondering to yourself how the heck this happened.

What you need to do is to hold on to your original frame and not move on until they concede your point. You can choose to address other points after the current issue is settled. You should bring the discussion back to your frame by saying things like "Lets focus on the point, do not drift" or "We can discuss that next. Lets finish this first"

Reframing is very subtle if you are unskilled but obvious once you master it. Many shit tests are reframes.

For example:

You: "Your friend Millie is pretty" Simple observation about third party

Her: "Do you think she's prettier than me?" Reframed to include herself and making this about competition

You: "Don't make this about you" Hold frame, keep it to simple observation

Example 2:

You: "You tell everyone at work what to do!" Observation/remark

Her: "Are you saying I'm bossy?" Reframe to insult, to see if you apologize

You: "I'm saying you show leadership. Take the compliment; I give them sparingly" Reframe it yourself!

State control is holding your emotional state of amused mastery/general coolness and not letting things others say and do flip you into a different emotional state. Holding state enables you to reframe/hold frame with mastery. The more emotional they can make you, the harder it is to hold frame and weaker you appear.

TLDR: Stay cool, hold frame.