Even if you give him missing the joke. Bug as used colloquially refers to spiders and insects, not just true bugs. There is a reason why true bugs have to be called true bugs.
The Hemiptera are called 'true' bugs because everyone - entomologists included - tend to call all insects 'bugs'. That is a loose term, whereas the true bugs are just those contained within the insect order Hemiptera.
He'd only be missing the joke if the spider's preferred beer was True Bug Lite.