Why should you try to move to your right when steering in an emergency?

Where to steer: If an oncoming driver has drifted into your lane, a move to your right is best. If that driver realizes what has happened, the natural response will be to return to his/her own lane. If something is blocking your path, the best direction to steer will depend on the situation.
If you have been using your mirrors, you will know which lane is empty and can be safely used.
If the shoulder is clear, going right may be best. No one is likely to be driving on the shoulder, but someone may be passing you on the left. You will know if you have been using your mirrors.
If you are blocked on both sides, a move to the right may be best. At least you will not force anyone into an opposing traffic lane and a possible head-on collision.