I've noticed that if you are going to be making a comment about what is going on in the moment, (especially when you have a personal investment in the outcome of the course of events that may follow,) it's very tricky to make your motive be understood when your motive is the intention for mutual insight. I find that it works best to prepare the ground to be received in the spirit of what you are about to say before you say it. So linguisticallly, the first skill is called "reframing." You must redefine the frame for the audience, because it is quite likely that they will misunderstand you if you assume they are on the same page as you are.
There is also a time of arrival factor that is also important. Once people are locked into repeating a vicious circle, it's very tricky to stop repeating what is the problem. Better to wait for another time when the vicious circle is about to happen, and make your attempt to interrupt the event that you can recognize is ABOUT to happen at that time...because this sort of thing will happen again and again if it really is a problem.
Often saying something will have no effect, because the action that is going on is that people are saying something - content is being ignored. So for the content of what is being said to have an effect, communication works better if you can figure out a creative way to "change the game" of HOW the content is being delivered. This is another form of reframing. Otherwise, whatever you say will just be reacted to as if it's merely a brand of violent defense or retort driven by the interpretation of some sort of paranoid motive - the sort which is left up to the negative imagination of the person on the defensive who doesn't have enough creative ability to imagine any possible positive constructive motives for your actions.
So this is another skill that I have learned to cultivate - the ability to imagine, under duress, multiple creative, reasonable explanation for the other person's actions when it "makes no sense" that they are in conflict, not becoming violent and getting upset. This is quite a challenge because anger and other emotions tend to block creativity.