The vast majority of fighters have an orthodox stance. That means that their left leg is their lead leg. Usually their sparring partners will also be orthodox so that is what they get used to.
Then comes along a southpaw and that throws a bit of a wrench in their strategy. Now they may be getting hit with more crosses and hooks than their used to, and their jab may be a little less effective. The game changes quite a bit.
The Southpaw vs Orthodox Strategy Simplified
If you are an orthodox fighter that wants to learn how to fight a southpaw or vice versa, there is one key principle to keep in mind. Get your lead leg to the outside of their lead leg!
By stepping to the outside of your opponent, you are setting up your cross and killing theirs. Also, you put yourself in a great position to kick, knee or elbow.
Checkout the video below to see what I am talking about.