The rhetoric around the Covid-19 vaccine is very strange and contradictory

Some time ago Joe Biden addressed the nation with a speech about the efficacy and importance of the Covid-19 vaccination.

He described how effective the vaccine is at protecting people from the disease. He told how only about one in a thousand vaccinated people get any symptoms from contracting Covid-19, and only one in like a hundred thousand need to be hospitalized (if I remember the numbers correctly. Even if they aren't the exact numbers he mentioned, they were in that order of magnitude.) He reassured people about how safe and effective the vaccine is.

Then, in the very next sentence he talked about how "unvaccinated people put us all in risk". He talked about how dangerous it is for some people to refuse to get vaccinated, and how they are a danger to everybody.

Wait... what?

First he tells how well the vaccine protects people against the disease... and then immediately after he says how dangerous it is for everybody if the disease is still being spread by unvaccinated people. He didn't say that unvaccinated people are a danger to other unvaccinated people. He said that they are a danger to everybody. "They put us all in risk", as in, every person, he himself included.

But if the vaccine is so effective at preventing the dangers of the disease, how exactly are unvaccinated people putting everybody in danger? How does that work?

He is not the only person talking like this. He was just parroting the general narrative about it. You can hear it all the time. People telling how effective the vaccine is and, on the same breath, telling how dangerous it is for everybody if people don't vaccinate themselves. Not just dangerous to themselves, not just dangerous to other unvaccinated people, but for everybody. Many other country leaders (such as Justin Trudeau), politicians and other influential people are saying the same thing.

They seem completely oblivious to the contradiction.

(For the record: This is not an anti-vaccine message. I'm most definitely not against the vaccine. I just find this self-contradicting rhetoric very strange, curious and hilarious.)