what will make people realise that kids are safe to go back to school as are their parents and their teachers
They're not "safe" in some absolute way, they're just "safer than they were a while ago", and (possibly) "safe enough that there's now more harm caused by all children staying in lockdown than by some children going back to school".
There's debate about all of these, there's no objectively right answer.
Quite a few people now have anecdotal experience either of hearing of cases with severe illness, hospitalisation or death, or they know friends or family who've been unwell for weeks even if they're recovering. Then you have families with vulnerable family members. And on top of that, rare but serious, is the new rare complication in children. And then the stories about blood clots and strokes in people who otherwise have mild symptoms.
Collectively, all of those things mean that lots of people are not YET going to be comfortable with a message that seems to be "they might catch it but they'll be fine". (They might well be by further on in the pandemic, if more is known about the disease and doctors can pinpoint which people are going to be severely affected and which aren't.)
But that's OK, because we can instead reassure people by saying "don't worry, you're very unlikely to catch it". That can be true, and it can be true quite soon, if we get low local rates of infection and really good testing, tracking and tracing.
It is still rational to want to avoid catching this virus if at all possible. There are still too many unknowns. Getting cross with people because they're not relaxed about it isn't going to work at this stage.
Reassuring people that we're working really hard to keep the amount of infection in the community as low as possible (it won't ever be zero), and that testing and tracking will help us squash new local outbreaks quickly, has a chance of working.
We're not quite there yet with the testing and tracking in this country, but people might be a lot more reassured when they've seen it in action, and when they can also see that our excess deaths are much lower than they are now. When that's true (soon I hope), schools will clearly be safer than they are right now - and possibly, safe enough for a lot more people.