From what I can piece together, picking up the option was a hedge against RGIII improving and growing into a competent starter. At that point in time that was the team's hope and the plan they were working on. If RGIII became even a mediocre starter, his $16 million price tag in 2016 would have been a good deal for the team.
Of course, he didn't improve, so the team lost on its bet. Easy to criticize in retrospect.
As for not cutting him, I think Rich Tandler made some good points:
http://realredskins.com/2015/09/03/need ... he-roster/A summary:
- They'll be paying him anyway.
- If they cut him, we might pay him to play for a division rival (ala DeSean Jackson, who was paid more money by the Eagles than the Redskins in 2014).
- Injuries to Cousins and/or McCoy might make starting RGIII the Skins best option — hard to do that when he's not on the team!
- Griffin is still young and this is just another chance for him to try to grow out of his issues. McCloughan has said before that he doesn't like giving up on young QBs. (Especially when you are paying him anyway.)
- No teams interested in trading for him right now, but that can change with injuries early in the season. Trade value might develop, and we'd look like idiots if we cut RGIII for no reason when we could have just held onto him for a few weeks and then gotten draft picks in return.