Coming back to this, as i think it is possible that there are different meanings of 'schools being closed' that may be leading to more heat than light.
One type of school closure is proactive - as part of an overall lockdown strategy, a school, schools in a particular area or nationwide will move through the 'tiers' that we announced by the government just before the bank Holiday (Tier 1 - current situation of all schools open; Tier 2, secondaries blended learning, primaries in; Tier 3, secondaries full home learning, primaries in; Tier 4, both primary and secondary schools home learning). As no particular triggers for each 'tier' were announced, then these decisions are essentially political, though based on public health.
Another type of school closure or part-closure is reactive - in response to actual infections within a school, whether of staff or students, a group, a class, year group or school are sent home to self-isolate for 14 days.
There are yet further closures that are consequential - where, due to cases in other schools or elsewhere in the community, insufficient staff are available to run the school because so many are isolating.
As I understand it, I don't think that anyone is arguing that reactive closures shouldn't happen, in order to curb the spread of the virus following a confirmed case or cases. There is some discussion / disagreement about the number of cases that trigger the closure, but I am not sure that anyone, faced with multiple cases within an environment like a school, is advocating carrying on exactly as normal.
Consequential closures are difficult, because they are hard t avoid or plan for. A large number of the closures just before lockdown were consequential as well as reactive - we had a couple of cases amongst the staff, and many amongst student families, around that date, but a much larger number of staff and students were absent because they were isolating with family members..
The disagreement is, I think, about whether any proactive closures are advisable - and to what extent they will become indistinguishable on the ground from a very large number of reactive closures.