I think people should get vaccinated, but 'think of the children' is not a strong argument since they seem to be at very low risk of becoming seriously ill or death compared to every other age category.
I was discussing in a more general context of vaccination rights/obligations, even though for the particular case of Covid19 you are right.
Note however that we still don't know exactly what long-term consequences Covid19 may have, so even with this, if we can avoid infecting young children, we should.