There are lots of studies and I'm working on reviewing and compiling them just for my own understanding. The upshot is that it's clear that
kids do transmit Coronavirus. However, they do not readily transmit to each other and in general, are not super-spreaders. By age 12, though, most kids are capable of doing a pretty good job of spreading CV in an enclosed space. By age 12, kids in contact sports or who are bused various places, are definitely transmitting to each other (but not at the rate of full grown adults).
30 kids in a room, with 10 of them silent transmitters of CoVid (easy to imagine), are certainly infectious to any adults in the room - and the room itself is probably infectious for at least a whole school day.
There are a bunch of unanswered questions, because we shut schools down early. But you can google CoVid Summer Camps and see that both kids and counselors have had (large) outbreaks. And schools in France, Italy and Israel (just off the top of my head) have seen outbreaks.
Kids are mostly infected by adults, IMO, but a couple of kids in a small apartment seem more than capable of spreading to the adults - we just don't have the contact tracing data to establish this point.
244 kids in Israel have CoVid after returning to school.
Some districts close after outbreaks but don't say how many children were involved. (US)
70 French students get CoVid after returning to school
The controversy over kids and CoVid centers around the fact that most of the time, it seems kids are getting it from infectious adults and not from each other. In fact, both France and Switzerland firmly believe that kids 12 and under cannot transmit to each other, whereas swab studies done in hospitals show that some kids under 12 have plenty of virus to shed. French and Swiss schools have smaller classroom size, generally have windows that open, have not met during late fall or winter, etc. The kids who've gotten it, they believe, got it from their teachers.
What is increasingly worrisome, though, is that even asymptomatic kids are exhibiting lung damage and heart wall damage. Kids without underlying conditions seem vulnerable to these things as well.
So we don't want kids to get it. But even if kids do not readily transmit to adults or to other children, how do we keep adults in schools from transmitting it kids and to each other? Presumably 20-40% of infected teachers and staff would be asymptomatic. But they'd infect a lot of kids (and their own classrooms).
Arizona coronavirus: Three teachers who shared a classroom got Covid-19. One of them died - CNN
(^warning, above link contains prominent picture involving fishing...)
The CDC has a page on CoVid deaths by age - children do die of CoVid, it's just proportionately way fewer. You can still find lots of articles published in February saying "no children have died in China or France" but that changed, and so naturally, parents are quite scared and concerned.
Study is needed to understand whether a bunch of children who are infectious and in a closed space are likely to infect others, as opposed to individual children infecting others in outdoor or well ventilated settings.