I have been hearing this question a lot. More specifically, "Why should I reinforce when I am competing against them for overall victory?"

To me it boils down to 3 reasons:
1)To help make larger, more dynamic battledays for everyone
2)To meet new people. It's more fun killing those you know than just strangers.
3)Because you're helping YOUR army out as well. Let me direct you to the following section out of the simplified rulebook:
Reinforcement Rules
  1. On weeks when your army isn't fighting you can help your army earn up to 4 Campaign.
  2. To do this, join the Reinforcement Room channel in the area owned by the army you are paired with this week.
  3. For each whole quarter there are 8 or more reinforcements the Reinforcing Army will earn 1 Campaign point.
  4. Reinforcements must be ACTIVE on TS. Either fighting in battle or waiting in the reinforcement room. You will not be counted if you join the room and go idle.
  5. Reinforcing is first come, first serve. If you decline to reinforce when it is your turn you will be moved to the back of the line. Check the Reinforcement room channel description for the current list.
So you have the opportunity to not only help out 21CW and make new friend, but a chance to help your Division towards victory!