Rankings are based of elo.

If your elo is lower than him, he'll be getting the higher rank. Before you can take ranks you have to have a higher elo than your opponent.

Example: If you have 1610 elo and have a rank of 639 and your opponent has an elo of 1620 and has a rank of 1176, he'll obviously get your rank because he has the higher elo.

You can gain elo by winning more games. As far as I can understand, you get 1+ elo when you win and when you are in about 1600 - 1620 range. The more elo you have, the harder it is to gain elo when winning and the easier it is to lose elo.

Hope this helps.