The rule is in place to keep teams on a level playing field when injuries occur. Say when we play Chicago in week 2, we have 7 guys that can't suit up due to injury. That would leave us with 46 players that week. But Chicago only has 2 injured players...they have 51 "bodies" to play with. Limiting every team to 45 (46 now) active players is suppose to keep every team with the same number of healthy, active players every week. How they arrived at those numbers (45 and 46), I have no clue. They probably conducted studies on average number of injuries.
That is my understanding of the reasoning behind the active player rule.