How was she supposed to know? He took her there; it's his fault.
I admire Julie-san for calling him out:
"I bet you've killed a cockroach." Damn straight he has!
Not to mention the countless flies subject to be killed or maimed by his chopsticks as he whiled away his workday at Daniel's apartment complex. Miyagi "respect all living things" my ass.
Respecting all life does not equal vowing to never kill; for example, soldiers in past wars often prayed for their enemies upon killing them. A more current example is found in Faramir's speech to Sam and Frodo, from THE TWO TOWERS...
"His loyalty was no less than yours. You wonder what his name is, where he came from, who set him upon his quest...and if he really was evil at heart."
I found it illogical as well, just like other aspects of this movie.
Rarely have I heard of respect for life extending to cockroaches which are basically dirty and can spread disease and can proliferate like crazy if they have the chance.
Nobody wants cockroaches crawling around their food.
YES certain breeds of cockroaches are "farmed" for food in China but i think we can safely assume that this roach was not one of them.