It's not the assembly itself, but rather of WHAT it's being assembled.
As others have said, the AR series is like Legos. It's just assembly of pre-made, pre-existing parts.
Of course, there can be a problem with incorrect assembly, but problems such as this tend to be glaringly obvious right from the get-go, such as putting the hammer spring legs on the bottom of the receiver instead of on top of the trigger pin, etc. And someone who can't assemble an AR correctly really has no business building one in the first place.
Therefore, it's not really the building of the rifle itself that is a problem.
So what might it be?
His bash against "home assembly" is more of a bash against "el cheapo no-name low quality parts". THAT, I think, is the major reason many frankenguns might bite the dust, because the Lego Nature™ of the AR pretty much excludes any real gunsmithing. Low quality parts can be off dimension, made of significantly lower quality material, not of the proper hardness, stiffness, et al.
Parts that are of only "slightly" lesser quality may work fine by themselves, but take a slightly off disconnector, a slightly off hammer, and a slightly off trigger, and they might build up enough tolerance stacking. Or a mismachined upper receiver, which looks perfect upon visual examination, could cause mysterious bolt carrier binding. Problems such as these sound like something that this guy would apparently blame on the builder. However, this builder would be guilty not of improper assembly, but rather, of purchasing substandard materials.
A relatively intelligent monkey with an all-in-one wrench can assemble an AR properly. But it takes an entire industry to make those parts correctly, to the correct dimensions, of the correct materials and to the correct final quality.
That, I think, is where the real bugs lie.
Assembling something from a collection of separately bought parts requires one to be their own Quality Control Inspector. For many, this usually consists of taking the rifle out to the range and ripping a few boxes of American Express through it and declaring it good. Most of us know that this isn't a good enough test, though, at least not for a rifle with which to defend life.
However, by buying parts of known quality (either from experience, reptuation, or both), we can minimize the Quality Control aspect of the assembly process to the point where we only need to put it together; given proper assembly, it will be 'good' 99% of the time, just as good as a quality factory built AR-15.
At least, that's my two cents.
Does a dog have the Lego Nature™?