This isn't some inter generational war. From the NHS website:

There's a worry that introducing chickenpox vaccination for all children could increase the risk of chickenpox and shingles in adults.

While chickenpox during childhood is unpleasant, the vast majority of children recover quickly and easily. In adults, chickenpox is more severe and the risk of complications increases with age.

If a childhood chickenpox vaccination programme was introduced, people would not catch chickenpox as children because the infection would no longer circulate in areas where the majority of children had been vaccinated.

This would leave unvaccinated children susceptible to contracting chickenpox as adults, when they are more likely to develop a more severe infection or a secondary complication, or in pregnancy, when there is a risk of the infection harming the baby.

We could also see a significant increase in cases of shingles in adults. Being exposed to chickenpox as an adult – for example, through contact with infected children – boosts your immunity to shingles.

If you vaccinate children against chickenpox, you lose this natural boosting, so immunity in adults will drop and more shingles cases will occur.