Predicting outcome of games - how to make team 1/2 interchangable
Home field advantage is incredibly important in sports. If you always put the home team in the first column, your model will adjust the bias term accordingly. I've been doing this successfully for NBA and MLB models for several years now. Making the first team the home team also eliminates the need for an explicit home indicator variable and you'll be able to use "half" of the data like you've described. 

For rare neutral games like the Superbowl, you would need to create a mirror image of the data. In other words, present two rows for each game (team-A,team-B;team-B,team-A). When it's time to score you model, you can just arbitrarily pick one of the two records because they represent mirror opposite of the same thing. I've done this before for March Madness basketball games (all neutral courts), and this year (2016) my March Madness model was in the top 10% in Kaggle, so the technique works. 

Home field advantage is just one of the variables you'll need to make a good predictive model, but that's an answer for another question.