It's not that Arthur lacks faith in her to keep herself safe, it's that he lacks faith in everyone to take the proper precautions when dealing with vampires. He's seen the worst of what they can do, and in his experience all it takes is one wrong turn.

But he keeps his mouth shut for the time being, deciding that it's not worth arguing about. Especially now, when Nancy's already upset about the curse. So he just sighs and continues on in silence, waiting for the cue to turn a corner or stop in front of a building.