Tony's eyes don't leave the spider as Peter mentally catches up with what was happening- at least until he makes that stupid comment.

"You're not the one refusing to swear you won't hurt anyone. And don't make this personal, kid!" He glared back at the spider. "And how did you figure out it's name?"

If he aimed low, he might be able to hit something vital.. But more than likely with Peter having this kind of reaction the kid would just get in the way. Since when did Peter not trust his judgment on something like this?