The fact that Katniss and Peeta are training together has the advantage of making them comrades. They can also practice fighting with one another in order to improve their combat skills during the games.
Cons:
The disadvantage is that they are both aware of each other's abilities. This gives them a notion of who their competitors are. When they began to form a bond, they attempted to die at the same time because they would rather die than live without each other, setting in motion the chain of events that followed.
