How can an unvaccinated person sicken a bunch of vaccinated people?
Because vaccines don’t ficking work like that.
There is a substantial minority of the population who are more susceptible to certain diseases than everyone else, to the point where they can still get sick even when they are vaccinated. Those people rely on the pathogen which causes the disease not to be introduced into their bodies at all; for this to be ensured, everyone around them must also be vaccinated.
Vaccines work best in people who need them the least, the healthy and young. The least effective are the people who are most vulnerable, young children and the elderly.
The objective is to eliminate these diseases from existence by denying them as many opportunities to spread and reproduce as possible. When people don't get vaccinated, it provides the viruses with host to sustain itself and spread from.
The effectiveness then acts like a bullet proof vest and the virus like a shut gun. The vest doesn't cover your whole body, just like the vaccine doesn't protect everyone, or everyone completely.
I hope these analogies help to explain the process and not confuse people more.