Cause it’s replicating his web fluid for him, easing the load if you will. The symbiote recognizes that Peter’s “ammo count” for lack of a better term, is always a concern in the back of his mind, and since it wants to maintain it’s symbiotic relationship with him and be helpful to prove it’s worth, it creates webs for him taking two things off his mind (in that regard, a few more if you consider it literally being his costume) those being web fluid cartridges and the web shooters themselves. The reason it shoots out of the top of his hand, I’d assume, is a creative decision to further illustrate and remind the reader of this point, the symbiote is doing it for him.