I made my own telescope. I took a telescope-making class from John Dobson. The reason for the higher quality than commercially-available mirrors is because humans are better than machines at inducing a random element into the grinding process. As you make your grinding strokes, every ~10 strokes, you rotate the mirror. After doing this 10's of thousands of times (turbo-1 did mention that it takes time), there should be no preference as to the direction the mirror was rotated, so it will average into a spherical shape. A machine, which is told how often and how far to rotate the mirror is more likely to be less random, hence there will be some preferred directions, creating stigmatisms in the mirror. Even by hand it is easy to accidently introduce a stigmatism. The back of your mirror blank will have small chips in it, and if you unwittingly line up your favorite chip with the 12 o'clock position each time it comes around, you'll end up with a preferred direction. There will be more grind strokes than average in that direction.
That said, my mirror isn't as nice as a commercially-manufactured one. My first attempt produced me a less-than-satisfactory mirror. Through it, the Moon looks awesome. Star clusters look awesome. And deep sky objects look awesome. But if I throw in a high power eyepiece to look at Jupiter or Saturn, I find it impossible to focus on it.
After finishing the grinding, you should be left with a spherical mirror. But at the focal lengths we were making, there's not a huge difference between a parabola and a sphere. So the mirror could be parabolized in the polishing process. Although some classes are taught to use a "knife-edge" method (I'm not sure exactly what this is), we were encouraged to simply eyeball it. After all, if your eye can't tell the difference, then it's as perfect as it needs to be. That's why John Dobson would laugh at all the computerized methods. And if we weren't comfortable with eye-balling it, John Dobson would eyeball it for us. He would just aim your scope at a distant ceramic insulator on a telephone pole that had the Sun gleaming off it. He would scan across the mirror making sure all points came to the same focus.