The absence of meat in their diets must have weakened their immune systems. A lot of other things could have made John and Mary sick this winter. Maybe they've been around a bunch of sickly kids or they started working in a hospital and their immune systems aren't used to all those germs. The non sequitur fallacy means that you've made a conclusion that is not justified on the grounds given. These two fallacies are similar to yet another fallacy known as Jumping to Conclusions or Hasty Generalization which means that the evidence provided is not yet substantial enough to warrant the conclusion we've arrived at.
Women make lousy drivers.
Asians are good at mathematics. Scottish people are tight with money. White men can't jump. The next time you meet a tall African American youth, ask him or her if he or she plays basketball. You'll deserve the icy stare you get in return.