One vs two arm snatches

The reason for doing one arm snatches instead of using both hands on a barbell is this:
With one handed snatches things are a little off balance due to your having the weight in only your one hand. This results in your core muscles being utilized to stabilize your body without a large amount of weight being needed.

The expense of one dumbbell is also less than a barbell and weights.
Storage is also easy for just one item.