This can be tricky simply because the two bars on each side move back and forth slightly, and decrease in size as you push them closer to the edge.
The best time to move is when the bar is moving away from your cursor on that side. As it moves away (towards the edge), push towards it slightly and it will move that way with you. Be careful not to move too far or it will slide back towards you too much and go past your cursor (and go back to the middle), which means you have to try it again.
If you're having trouble, try doing just one at a time. Once you get one side all the way to the edge, you can just leave it alone. As long as you don't move the cursor on that side, it won't go back to the middle. Then you can focus on the other side.
Once you get both of the green bars past the lines at the edges, you will successfully break up the fight. Just be patient and go slow. Trying to speed through this will surely cause you to fail.