My concern is that it creates confusion at the intersection. It's a 3 way stop with the street he and I were on being the one that t-bones. Yesterday when I arrived I was traveling west as was the boy. He wanted to turn left and I needed to turn right. There was 3 cars heading south and 2 cars heading north. He waved through the first car heading south, and everyone waited for him to go, but he waved through a car heading north. Again everyone waited for him to go but he waved through another car and then another car with each time the new car arriving at the intersection and indicating for him to go. Only after all the cross cars were clear did he notice me behing him and then indicated for me to go around him to turn right. By this time another car had arrived behind me and another was approaching the from the north. I didn't wait to see if he was going to finally take his turn.
The other two days there wasn't as much traffic so his actions weren't as notable. But yesterday's created confusion for all drivers. All were patient, but it does concern me about an impatient driver getting caught up in the confusion.
I'm sure the kid is just trying to be safe by waiting for the cars to clear out, but I think you're right to be concerned. IMO, a bike safety talk would probably be good for this kid, so letting the school know it would be useful to offer one would be appropriate. Not to get the kid in trouble--he's clearly trying to ride safely--but so someone will teach him even better ways to ride safely.
The problem is that he's putting himself in a gray zone between a vehicle (with a specific place in the three-way stop queue) and a non-vehicle (who would be off the road and not part of the normal three-way stop queue). That gray zone can be dangerous because it's unpredictable. There's a defined order for going through a three-way stop for good reason. When you start changing up the order by waving people through when it's not their turn, it makes the situation less predictable and you have to count on everyone properly interpreting hand signals, which isn't exactly a precise form of communication.
IMO there are three good options for handling the three-way intersection on a bike. 1) Take your turn like the other vehicles, after checking to make sure that all the cars are stopping/stopped. 2) Get off of the bike and move out of the road, so you can cross the intersection as a pedestrian (either waiting for all the cars to clear or crossing when the person with the right-of-way waves you through). 3) Get the bike completely out of the road (onto the sidewalk or grass) and step back, so it's clear you're out of the queue, and wait for cars to clear before getting back on the road and riding through.
The problem in the OP is that he stays on the road (so the cars can't assume he's completely out of the queue and proceed as if he wasn't there), but he also isn't taking his turn, so he's messing up the normal order. From the OP's description, he ended up acting as "traffic cop" for the intersection, waving each person through, and the OP ended up missing her turn in the rotation because she was behind him and he was waving other people through instead. That's where it gets unsafe. If he doesn't want to go, he needs to move out of the way completely and let the system proceed without him.