The mechanism behind why more fiber helps is pretty straightforward:

Insoluble fiber speeds up gut motility. Faster gut motility means less time for toxins to sit and absorb in your gut.

Also, fermentable fibers serve as substrate for gut microbes, producing short-chain fatty acids (butyrate is one - a primary fuel source for colonocytes - the cells that line your colon).

It also lowers colonic pH, inhibiting pathogenic bacteria.

Lastly, (although there are tons more benefits I'm not listing), soluble fiber is incredible for people trying to lose weight, as highly fibrous foods increase satiety, keeping you fuller for longer.

Uh, what? I have not made a presuppositional argument (I made no argument at all...). I made a statement about my epistemic state - ie: that I would "bet" on low fiber being the major contributor to colon cancer rates. Someone then asserted that it can't be that, and I asked "why?".

> Why would more fiber help?

Because there is an incredible amount of research into high fiber diets being good for your gut, including reduced colon cancer rates. This is the consensus of various organizations such as WHO - high fiber diets have lower risks of colon cancer.