(1) the quarterback position is the least demanding athletically on the whole body: Yes, QBs have strong arms but they don't need to have whole-body strength and speed like running backs and wide receivers. The players in non-QB positions have a peak of ~5 years and then quickly drop off from wear & tear. The QB position depends more on intellect -- "reading the field" and making quick decisions to get rid of the ball -- rather than running all over the field. Similar reason to why place kickers who just kick field goals can have longer careers than running backs.
(2) the particular style Tom Brady plays: he plays in a deliberate "low injury risk" way. He very rarely "scrambles" (runs out of the pocket). Scrambling opens up the quarterback to violent hits from defenders causing season-ending knee and ankle injuries. Famous scramblers that had horrific injuries include Randall Cunningham, Robert Griffin III, etc. Tom Brady got his big chance in the NFL because the QB he replaced (Drew Bledsoe) got injured during a scramble. During a play, Brady stays very aware of the offensive live protection collapsing around him and he instantly tucks the ball and crumples his body. This means he doesn't get body slammed to the ground while his arm is in mid-throwing motion, or get his knees/ankles crushed by defenders.
(3) NFL rules that evolved to protect the quarterback more and more: A 1980s quarterback like Dan Marino would get more physically punished by rushing defenders than today's quarterbacks like Tom Brady. The NFL added stricter rules because the quarterbacks are the highest-profile "stars" of the league so having them not playing on tv because of injuries is not in their best interest.