Giving up and just letting the virus spread is just not an option. So we're stuck with adjusting our behaviour, testing, tracking etc. Testing isn't perfect but should improve. Knowledge of how the virus works and the disease progress will improve. But those things will work. We can get rates low, and track where the disease is,and behave in ways that reduce transmission. We don't have to keep schools closed forever to do that, but neither is there anything special about June 1st in particular, or about the particular classes going back first.
It's fine to want your children to go back then, and it's fine not to want to. Neither is wrong.
The government, on the other hand, might be wrong in telling us it's fine on June 1st in particular, might be underestimating how risky it is from the point of view of restarting rapid transmission, might have picked classes based on childcare rather than public health... I don't know. I'm not convinced it's quite right, even if the basic idea of trying to get schools functioning for more pupils is good.