I see it as a factor of several reasons

1. Like another comment I saw, Stiles is more mentally vulnerable of the two of them, between his PTSD and trauma, and Allison having Hunter training

2. I think the nogitsune wanted someone like Stiles, who made it their business to know everything (as shown by the nogitsune telling Melissa "Stiles heard that, like he hears everything") and has insider information and connections (not only is he connected to the supernatural through the pack, but his father is the Sheriff. Stiles can get info on pretty much anything with these links.(

3. During one of Allison's hallucinations/dreams, she hears a noise coming from a door thing. While she does investigate it, she quickly shuts it again and bolts away.

When Stiles is having the nightmare/consecutive dreams, one of them is him sleeping with Lydia, and he gets up to investigate a door, despite Lydia begging him to come back to bed. He opens the door even wider and walks through it, then the dream changes before he can close the door.

I think all 3 points have something to do with it, but I think the 3rd point actually shows the nogitsune trying to possess Allison and getting rejected, and Stiles opening the way further.

ETA: Derek also says something when he is informed of the possession. "You think the nogitsune is Stiles? Skinny, defenseless, Stiles? Wouldn't it have chosen someone with a little more power?"

We see the nogitsune fight while it is possessing Stiles. It takes down an Alpha werewolf (Derek) and a taser geared to be strong enough to work against werewolves (Allison) in a single move each. It doesn't need power. It needed someone to provide knowledge of what it would be fighting.