It comes down to transmissibility. If the vaccine stops you from transmitting the virus, then as many as possible need the vaccination.
The vaccination has a 70-90% chance of preventing the virus. If 1,000,000 people over 65 get vaccinated and no young people get vaccinated, then there's still 100,000 - 300,000 at risk of death from the virus, and it's likely that 3,000 - 10,000 people who will likely die. Of course there's a lot more than 1,000,000 people over 65 in the world. So those stats would go up significantly. Plus there's the fact that young people do die. They're just at a much lower chance of dying compared to the older people.
All that said, we don't yet know if the vaccine will prevent transmission, but it looks like it'll at least reduce it by around 50%.