McCown is nobody's idea of a great backup quarterback. The 31-year-old has thrown nine touchdowns and 14 picks in his eight year NFL career, and he was a disaster in Jacksonville last year. But there's a perfectly sane, uncontroversial reason the Falcons want him backing up Ryan. It has everything to do with experience.
Whatever his faults, McCown has spent multiple seasons under Dirk Koetter and is comfortable with his offense. He may not be particularly good in that offense, but he's familiar with it. The Falcons are keeping him around to hold down the backup job until Dominique Davis grows into the role and fully learns the offense. They don't want to be caught with a rookie who, for all his prodigious talents, would struggle to run a complex offense. Thus, McCown.
I fully expect Davis to overtake McCown by the end of the season, but for now, the coaching staff believes he's the best option. Let's hope they're right, and that the point is moot because Matt Ryan is healthy and effective.