Because they wanted to get somewhere?
Mr. R was on a flight last year where a man was vomiting into the trash can at the gate. The GA informed the passengers this man would not be boarding. Well, guess who ended up sitting directly behind Mr. R? This man vomited several times during the flight. I feel very sorry for the person sitting next to him, and there was a woman sitting there on the very full flight.
I don't think people who are so obviously ill should be allowed to board a flight. I did see an older man in BUD this summer, who was so drunk he could hardly stand up. He kept going up to an older woman and was trying to hug and sing to her. He was prevented from boarding at least, because I just know he would have been seated next to me!
At least he was not contagious and was somewhat entertaining.