This guy is usually pretty reliable, but he is way off base here. Of course electorns spin.
His main argument is that if you conceptualize an electron as a particle, then it is hard to see how the charge distribution and angular velocity could result in the observed magnetic moment.
Okay, electrons are not classical particles. If you conceptualize an electron as a classical particle, you will have trouble with position, momentum, and everything else.
Spin is the intrinsic angular momentum, quantized.
Update: I found this explanation:
WHAT IS SPIN?These arguments are just wrong.
Spin is an inherent property possessed by the electron. However, it does not rotate. In quantum mechanics, we speak of an en electron as having an intrinsic angular momentum called spin. The reason we use this term is that electrons possess an angular momentum & a magnetic moment just like a rotating charged body.
DO ELECTRONS SPIN SIMILAR TO PLANETS?
IT IS MISLEADING TO IMAGINE AN ELECTRON AS A SMALL SPINNING OBJECT DUE TO THE FOLLOWING:
An electron’s spin is quantified. It has only two possible orientations, spin up and down, unlike a tossed ball.
To regard an electron as spinning, it must rotate with a speed greater than light to have the correct angular momentum[Griffiths, 2005, problem 4.25].
Similarly, the electron’s charge would have to rotate faster than the speed of light to generate the correct magnetic moment[Rohrlich, 2007, Pg 127].
Unlike a tossed ball, the spin of an electron never changes. It has only two possible orientations: spin up and down.
The 1st and 4th are not true. An electron spin can be in any direction, not just up and down. If you put it in a suitable magnetic field, then it will be just up or down, but the same is true about a classical spinning charged ball.
I don't have those textbooks, but they presumably do a computation assuming an electron is a charged particle with extremely small size. But an electron is not a classical particle. While it looks like a point particle in some experiments, it also looks like a wave of concentrated fields. That wave/field is spinning.