But spider-silk being produced inside his body, which requires an entire circulatory system reconfiguration, and coming out of his
wrists (???), is completely fine.
The USM explanation is close in concept, but it still deviates to convenient storytelling. Dad works on special formula for years and years, and his son gets bitten by a genetically altered spider that coincidentally relates to said formula? Yeah, not into that.
I'd much rather Peter
steal research material from the same labs that were working on the spiders. After getting bit, he experiences these newfound powers and being somewhat of a genius himself, wants to figure out what the hell is going on. A scientific team doing genetic research on arachnids would most likely be studying spider-silk and the means to reproduce it for industrial uses. That's half the work done. Borrowing from USM at this point, Peter completes the formula from the combination of being a science wiz, and having the innate know-how to reproduce specialized protein fibers. Anyone questioning that last bit should read my previous post about pre-disposed genetic traits.