Why do astronauts have to quarantine?

There's no infirmary on board, nor any chance of a quick trip home. A minor infection becomes more persistent in weightlessness, because the sinuses don't drain well; it can spread quickly to the whole crew in the cabin's recirculated air and, in the worst case, jeopardize a docking maneuver or a spacewalk. The Apollo era left the clearest examples: the Apollo 7 crew spent the mission with severe colds, and before Apollo 13, Ken Mattingly had to be replaced at the last minute because he had been in contact with a case of rubella.

Since then, crews live in isolation before liftoff: a small circle of people, periodic medical checks, controlled housing, distance from family and the public. Anyone who, for professional reasons, has close contact with the crew also enters this health program. The goal isn't to prevent every possible infection, but to catch an illness while the crew is still on the ground, rather than have it break out already in orbit, where it would be neither easy to treat nor to contain.

On the first Moon landings, a second quarantine was added, of an entirely opposite nature: no one could rule out that lunar rocks and dust might bring microorganisms back to Earth. That's why returning astronauts were isolated right after splashdown, moved to a laboratory in a modified trailer, and observed there along with the samples. Once the analyses showed no sign of life, NASA dropped this return quarantine on later Moon missions.