It’s not the Federal government that is forcing it on anyone. It’s the states and the habit predates the Federal government.
FYI, General George Washington required mandatory smallpox vaccination of his soldiers.
A separate article noted that mandatory vaccination differs from compulsory vaccination. With mandatory vaccination, people might have to pay a fine (like Henning Jacobson) or they might be prohibited from attending school (like Rosalyn Zucht) or from working in a particular hospital or business. With compulsory vaccination, on the other hand, people are vaccinated against their will or children are vaccinated against their parents will.
The article noted a recent example of compulsory vaccination occurred in Philadelphia, where parents withholding vaccines on religious grounds (which state law permitted) were taken to court. The ACLU refused to defend the parents (surprise) and the kids were immunized on "public health" concerns.
It seems it's only a matter of time before someone uses this flimsy thinking to force gun confiscation as a public health matter.