Self teaching is better for some things than others. You wouldn't be able to teach yourself to be something as broad as electrical engineering. But if you already have that background, not as hard to self-teach a particular skill.
I'm completely self taught in taxation. But I did have some background to start with. My dad is also an EA, and I had been preparing tax returns as a sideline since I was in high school.
In the 90's, most accounting and law schools didn't even offer courses in personal taxation. If they did, it was a one semester elective. Accountants are required to take classes on entity taxation, and lawyers are required to take a course in estate/trust taxation. To this day, personal taxation, which is over 1/2 of the tax code, continues to get short shrift.
When I applied to take the IRS Special Enrollment Examinations (required to become an Enrolled Agent--four exams given over 2 days, and you must pass all four, each independently), the IRS sent me a large box. One of those 30 inch cube boxes packed full of IRS publications. There was a letter inside which basically said "Thank you for applying. Now read these."
So I put together a comprehensive course of study for myself, and took the exams. A few weeks later, I got a letter telling me that I had passed, along with corrected copies of my answer sheets. The pass threshhold that year was 63% (they set the passing bar low because even then the pass rate is usually below 15%). My composite score was 88%. A few weeks after that, I got a letter from Commissioner Rossotti congratulating me on finishing in the top 20. Eventually, they even sent me my enrollment certificate and card.
So, it's actually possible to teach yourself a profession if you have some background.
If anyone is interested in becoming an EA, let me know. I can mentor. Especially if you live in Denver. I may be taking on an associate soon.