Originally Posted by
MasterOfMoogles
For example, he wanted to bring Klein with him in the beginning, but Klein wanted to stay with his friends so Kirito left because it would've been too dangerous with all of them.
In this case, Kirito knows Death Gun is targeting strong players, so anyone at the BoB finals would potentially be fair game. By sticking with a potential target he both increases his odds of reaching his goal and can protect her at the same time if need be. The situation is actually kind of similar Scilica's story, except Sinon isn't useless and there are a lot of potential targets.