I'm not a military thinker, so I might well be off on this, but I'd say because that would usually results in a draw, whereas the commanding officers generally

I'm not a military thinker, so I might well be off on this, but I'd say because that would usually results in a draw, whereas the commanding officers generally want to win so that they can achieve the overall plan set out by strategic command - and want to achieve a crushing victory from which the opponent cannot recover from. I guess an army on the retreat who would favor an instant draw would favor the fraternizing, but generally by that point the winning army - including the soldiers - are not amenable to stop their advance and play a friendly game of football.