The problem you're most likely having is that nobody else is trying to play co-op at the same time. It's an old game and most people are playing multiplayer or the campaign, not co-op.
Unless somebody else is searching for a co-op game at the same time that you are it won't start. I think last time I tried it took an hour to find a game lol. If you can find somebody else that wants to play co-op (maybe here on TBG site/discord or on the /r/battlefield3 reddit) you can add them on battlelog as a friend and then team up.