I think the issue is being "out."
Thank you for identifying the “issue“ for me, because I’m so new here.

Polyamory is so new, novel, misunderstood, held in suspicion by the general public (as being gay/queer was, and still is, in many cases), that the poly (or queer) person in question will come out selectively, just to protect themselves.
New, novel and misunderstood?? Open marriages seem to have been around for at least 100-150 yrs ,if not longer. IS the nuance of polyamory that difficult to understand?
We have many many threads here about the dynamics of being a parent while practicing polyamory. It's not so black and white as "never lie, period."
I wasn’t suggesting black or white. I was suggesting discussing with his wife, which was more important to them to start telling lies about this new dynamic shift, or being out within the family, or at least the 13yr old, because nothing good will come if the kid suspects, sees, hears things that suggests one of his parents is having an affair. The automatic assumption is there is a betrayal going on, which causes a conflict in loyalties, and then if and when caught, what will be the fall out, divorce, like some of my friends.
There's this thing called being discreet.
Again thank you for this. It doesn’t feel too condescending. I invite you to look up the definition of discreet and see if openly lying is part of that.
Especially when you're new to polyamory yourself, and barely know what you are doing, it's hard to explain it sensitively to kids, especially teens, who understand sex. With very young children, it's easier, as you can ignore the whole sex topic.
Everything about transitioning from mono to poly is hard. This is just one more thing that needs to be dealt with. Choices and consequences is all I’m saying. Which one could be worse in the end?
I’m sure one of the poly family therapists or child psychologists that are poly, or treat kids struggling, have put out pamphlets or blueprints as to how to come out to your children. And really, how sensitive does this have to be? Mom and Dad sit down together with the child and announce, "For a list of private reasons, we don’t want to remain exclusive romantically or sexually, and this small change makes us more happy and satisfied as a married couple and thus as a family." Hopefully this all works out to be true, but it’s a starting baseline.
And, as parents, even mono ones, having to explain sex paraphernalia to kids isn't that easy, lol. I wouldn't be so quick to just blow this off as, "Of course, explain immediately in the car that Dad is carrying on sexually with someone else who is not Mommy."
Who’s suggesting blowing this off with some immediate explanation???? WTF