If you strain, then you don't have to use vinegar.
Swirl the water, but gently.
If you swirl it too little, too slowly, then the eggs sink to the bottom, the yolk stays in contact with the bottom for a while, and the yolk becomes overcooked. And swirling helps the egg flip over at some point, which also helps avoid the yolk being overcooked.
If you swirl it too fast, then the inner egg whites begin separating from the yolk, and the final cooked egg splits apart into pieces instead of being one cohesive whole.