For healthy children, getting covid is most often not a big deal. Typically they will get mild or no symptoms, however for an unlucky few, it can be a serious disease.
In regards directly protecting children from illness, there is a relatively small benefit as most of them would not get very sick anyway.
HOWEVER
If covid runs riot through a school, it can bring about serious disruption to the school, and teachers and other staff - especially any staff member with a medical reason why they cannot be vaccinated are placed in far greater risk if high levels of covid are circulating.
Vaccination does not totally stop people from picking up the virus, or completely eliminate the risk they might transmit it, however it does massively reduce illness and death in the vaccinated, and vaccinated people will usually not shed as much virus or shed it for as long as if they were unvaccinated.
Covid vaccine is very well tolerated by children with very few side effects, and I for one believe that the more people we have fully vaccinated, the less people will get sick or die of covid, and the lower the levels of transmission are likely to be in the general community.
In short, do children need the vaccine to directly protect them from serious illness? Not essential but nice to have.
Do children need the vaccine to help keep the schools open and minimise disruption to their education? I believe so.
Do children need to be vaccinated to help make everyone else including their elderly relatives a little safer? I believe there is a strong case.
Are children age 12 to 16 able to decide for themselves? There is a legal test called Gillick competency - which basically means that if a child is able to understand what a vaccine is, consider the benefits and possible risks and with that knowledge come to an informed decision, then in law it is their decision and if a Gillick competent 12 year old asks to have the vaccine even though their parents are anti-vaxers, then they can accept the vaccine and their parents are not able to overturn that decision.