People need to get their heads around the absolute inevitability of a second wave. Probably even a third or fourth, but the second is an absolute cert to happen.
That's not the reason schools shouldn't re-open - it's because if you are taking active measures to suppress the virus across the country then you need a consistent message for the population to adhere to rules and you need the plan to be as comprehensive as possible but also as short as possible, as people get fatigued and start to not listen unless you have an authoritarian government who would shoot you in the head if you don't.
If you open schools, you are no longer locked down. If they lift the entire lockdown, fine. It'd be a mistake and you'd hasten a massive spike in deaths, but whatever, that's the governments mistake to make. But if you pretend the lockdown is still happening and just open schools and expect everyone to carry on staying indoors or to observe social distancing, they won't - and to make matters worse, when the second spike does happen and you reintroduce lockdown after, what, 2-4 weeks of lifting it, everyone will be annoyed and less likely to listen.
The TLDR version - either end the lockdown and open schools, or keep it and don't. If you're going to ease the lockdown, there's many measures to take beforehand - open beer gardens, outdoor spaces for restaurants etc. But opening schools isn't one of those options; it's an economic decision.