Self-taught, while not always, usually means all syntax and APIs but precious little theory except that which is obtained through osmosis. Due to the "you don't know what you don't know" factor this limits not only the domain of problems that can be solved but the efficiency, robustness and maintainability of their solutions. Most often they reflect a focus on too many trees and far too few forests. A reflection similar to their decision to try to shortcut their way around the prerequisite of a formal education.
Mean while anyone having to work with them or their products is forced to waste time waiting for the reinvention wheels as well as fixing or working around their messes.
Learning syntax and APIs are one thing. Maybe you're particularly adept at that. However, this is only a fraction of what makes a good software engineer. Theory is critical to their application. The development of robust, efficient, and maintainable software more than just knowing how to mash the keyboard and hit "compile". The theory of application for those APIs, the theory underlying data structures and algorithms, theories of architecture, etc.. With out these your projects will suffer as you constantly reinvent the wheel and "learn from your mistakes." Yet, those who went the self-teaching route most often skip the theory, skip the mental exercise, narrowly focusing on syntax and APIs.
I'm not saying a college degree is a perfect accommodation for producing best of breed software engineers. I think many colleges are missing the mark on providing necessary experiences encountered by those in the trenches. So much of the course work feels like bringing a tank to a knife fight and it provides a distorted sense of reality that undermines the point of what they're learning.
I find that most people trying to argue against math generally are doing so by asserting that if a certain math is not put to practice in the software that a person is developing that that math is unnecessary. It also seems to be commonly asserted that persons with a strong mathematical background are just being pretentious.
I believe that the anti-math crowd is missing the point. For a software developer it isn't the skill of solving calculus problems, but the skills required to solve calculus problems. What I mean by this is that in order to work to a solution for a given mathematical problem you are exercising many other skills. Skills such as logic, abstraction, visualization, etc. are very much employed in software development. You go to the gym not because you have aspirations of mastering a bench press, but because you aspire for a stronger, healthier body. Mathematics are an example of exercise equipment for a software developer.
He has not acquired a fortune; the fortune has acquired him. -- Bion