It's been explained quite a lot why the country is not vaccinating teachers.
It's because it won't lead to schools reopening during Alert 5 and lockdown. What we as a country need is to get off Alert 5 and that is done by taking pressure off the NHS by vaccinating those most at risk of serious illness or death. Only then do the numbers in hospitals come down and we can move to a lower level of Alert and get some economic activity going again.
Unless you want to prolong lockdown, and he close to intolerable stress on NHS at present, there isn't really an alternative.
Teachers are under consideration for highest occupational priority (alongside police and some others), and I think that is a thoroughly good idea.
But not earlier when it prolongs lockdown