Well technically, Rogan’s is kinda right, but saying it wrong.
The vaccine doesn’t directly cause mutations. Mutations occur naturally by chance. However, the presence of the vaccine in the ecosystem will impact natural selection in the original virus and the mutations that are resistant to the vaccine will increase in the ecosystem as the numbers of transmission in the original virus decrease making the variant resistant strain become the dominant strain the ecosystem because the resistant ones still have the ability to be transmitted.
This is why there’s a new flu shot every year because viruses adapt to the environment just like organisms. Same thing with pesticides, that’s why they have to make stronger pesticides every couple years because the resistant “pests” become the dominant mutation and a new pesticide has to be created to combat the resistant pests. And so on and so forth.
Harsh to say, but If we just let everyone whose supposed to die, die through natural selection there would be no need for a vaccine and no emergence of a variant to then therefore need a stronger or booster vaccine . And the human population will be stronger as a whole because of it.