Money. If you're spending $2.5k to $3k per year or more for a pair of season tickets, the chance to make back a couple of hundred bucks by selling a game or two isn't crazy. The two most obvious games that are candidates for selling tickets are the Monday game the Christmas Eve game (which has over 2,000 tickets for sale).
The Patriots are pretty high up there in terms of Sunday and Monday night games in the last few years, so it's not a new experience for many of the STHs. Add in the fact that it may be the most difficult stadium to get in and out of, and there's your answer.
Remember, with more than 50k season ticket holders, even if 98 percent don't put any game on ticketexchange, that's still 1,000 tickets.