You have to remember that, ultimately, this comes down to basic maths. The virus spreads by human to human contact and the more of those contacts that there are, the faster and further the virus can spread.
When we reopen schools in September, the current plan is to keep children and teachers in a 'bubble' within each school year. If each of those bubbles has, say, 250 people in it, then the number of potential human contacts is 31,125 (the number of pairs from 250).
When those children and teachers then go home at the end of the day, they probably come into contact with other children in the family, who've also had a potential 31,125 contacts. If someone in the household then goes to the pub for a couple of hours and sits in an enclosed space with 30 other people, that multiplies all of those previous contacts by a further 435. This all starts afresh the following day and so on.
As you can see, as we open up more, the number of potential contacts grows exponentially. Therefore, even though the risk of any individual contact spreading the virus may be incredibly small, once you've got large number of such contacts, it becomes a mathematical certainty that the virus will spread.
This is what the SAGE experts mean when they say there may need to be trade offs if we want to prioritise reopening schools in September. I wouldn't dismiss at as blown out of proportion and the people being quoted are the very people who will be advising the government accordingly.