Why can Cindy Moon (Silk) produce organic webbing while Peter Parker can't?

This is just a wild guess but since Silk is "The Bride" amongst the totems, is it possible that she has these ability along with the strengthen spider sense due to that fact? Again, just a wild guess. Think about it. In terms of Strength, Peter rises above, being "The Other". And it would seem that "The Bride" is some sort of counterpart to "The Other", obtaining the ability which the male counterpart lacks. Then again, this is just a guess of mine. Would like to actually know the truth though.

It may be just a theory, but I'm guessing "natural genetic variation" may be the best reason.

While their "arachnid totemic nature" may indeed have something to do with it [after all, Ezekiel, Peter's first Spider-Totem "mentor", had seemingly lesser strength, greater agility, but no kind of webbing, whatsoever, at least in his early appearances], it seems there is a range of natural difference between all the various spider-people. For example, the spider that was responsible for Miles Morales' powers also bestowed him with camouflage abilities and slight bio-electricity generation. Granted, this was a completely different spider from the one that bit the Peter Parker of that universe, and likely a different variation of the Oz. As such, everything from the species of the individual bug to formula differences could account for that variance in power.

With Silk, though, if you're looking for a genuine in-story reason, the only possible two could be:

1. Genetic difference: Every individual's bio-chemistry is vastly different, even within the same family; this is how you can have one sibling who is deathly allergic to a biological element [like, say, peanuts, diary, or shrimp]... and another to whom it has absolutely no effect. Now, both of these individuals should ideally have the same base genetic markers from both parents, but for whatever reason, something makes the expression of a gene which causes a histamine reaction within one sibling, which the other simply lacks. Cindy Moon my have just possessed the base genes to express "silk creation," or a higher likelihood of that gene being expressed as an ability for her. As this seems to be a power Cindy shows right off, this is strongly implied to be the case.
   This is interesting, as it implies that anyone bitten by that same spider would gain similar "base powers" [Superhuman strength, speed, agility, stamina, reflexes and endurance, and clinging to surfaces]--- but that those abilities would occur at different levels, much the way some people are just built naturally stronger or faster. How this would affect the difference in the strength of their spider senses, I'm not sure....but I'd like to think Ezekiel's training her for years had something more to do with that; we've already seen that Peter can "train" his spider sense to be more focused, simply by just closing his eyes and blocking all other sensory input, so that difference could be natural, or developed.

I use this analog specifically because, while not an "allergic reaction", the exposure to the very same stimulus [the irradiated venom in the spider bite], produced, in some ways, differing physical expressions or effects on two individuals [Peter and Cindy], where as her genetics made her more likely to develop the organic spinnerets than his did. Mind you, I'm guessing Cindy hasn't [yet] had to deal with a "Man-spider" [or "Woman-spider"] mutation or transformation yet, or some of the other physical alterations Peter has gone through as his powers have evolved. But that could also be due to the fact that she was essentially sealed in a bunker for years and thus didn't have all the other outside stimuli [from the physically taxing confrontations, to the various exposures to radiation and other energies] that Peter experienced.

Also, since Cindy was bitten after Peter, it could also be that the spider had just "continued mutating", and passed along an extra ability he'd only "just then" developed.

2. Gender Difference: Generally speaking, female spiders in nature tend to be larger in size and possess greater web generation capacity than their male counterparts, at least in certain species. It's not impossible then that Cindy's XX chromosomal nature allowed her to develop the ability more naturally.... but this would be discounted totally by the fact that Spider-Gwen doesn't spin silk of her own. However, if we look at other spider Women, "natural web generation" of one kind or another has been a common thing. This same gender difference, taking into account the actual scientifically studied and verifiable neurological profiles done in several studies, may also be a latent explanation for Cindy's greater spider-sense, as opposed to Ezekiel's training her. This hypothesis can be drawn from examples as follows:

A number of structural elements in the human brain differ between males and females. “Structural” refers to actual parts of the brain and the way they are built, including their size and/or mass....Females often have a larger hippocampus, our human memory center. Females also often have a higher density of neural connections into the hippocampus. As a result, girls and women tend to input or absorb more sensorial and emotive information than males do. By “sensorial” we mean information to and from all five senses. If you note your observations over the next months of boys and girls and women and men, you will find that females tend to sense a lot more of what is going on around them throughout the day, and they retain that sensorial information more than men do https://www.psychologytoday.com/us/blog/hope-relationships/201402/brain-differences-between-genders

While this doesn't speak to the webbing itself, it does provide a viable theoretic basis for the differences in power levels based solely around how the physical aspects of a body develop differently from males to females. So it's not an "impossibility"-----though admittedly with Spider-Gwen's presence, it's a lower likelihood----- that the this may have something to do with the Web generation, as well.

Of course, we are ignoring the simplest and most likely reason for this notable difference in Silk's power compared to Peters: Plot Demands.

It makes logical sense for Peter to have been able to "create" his webbing using science; the guy was a genius even as a kid, after all. Cindy doing so, however, would have been a bit too convenient, and with a name like "Silk" they kind of needed her to have webbing of a sort, especially as a means of making the stories easier [her making herself a costume on the fly, for instance]. So we could just chalk her web powers up to her "spider totem" status, and accept that different totems are afforded different abilities, and while they all have the base powers, what they get specifically can be something of a crap shoot.....

But admittedly, this is all speculation until Marvel itself makes some canon explanation.