Can't you read what I wrote? Your first sentence is exactly the opposite of what I said!
It is a home console, it is a handheld, it is both, it is a hybrid. It is NOT "not a home console", it is NOT "not a handheld".
The only thing we can say is that the Switch is not EXCLUSIVELY a home console. But that doesn't make it NOT a home console.
A home console, by definition, is a device dedicated to running games that are played on a TV. The Switch fits that definition, though it also fits the definition of a device dedicated to running games that are played on the go. So it's both, but not exclusively either or.
Otherwise, if we follow your logic, then the Switch is not even a handheld. A handheld is a machine dedicated to running games that can be played on the go. But the Switch isn't that. It is designed to be played at home, on a TV. The dock is an integral part of the system, not an accessory.
How is the switch designed to be played at home? The switch does not need a TV nor does it need to be plugged into a wall to work. That is what qualifies any device to be a handheld. The switch is (and I do not believe I have to even say this) is designed as a handheld first and foremost. The screen and battery it has is a big hint.
If you buy a switch and take it home, but don't have a TV in your house, can you still play your games?
Ok, now if you buy a PS4 and take it home but don't have a TV, can you play your games?
The answers to those questions are literally what makes one of those devices a home console, and one a handheld. The switch is simply a handheld, that can also be plugged into a TV. The fact that it has its own power source and displays literally means its a handheld.
I can take my laptop, (which mind you even comes with a built-in HDMI port (so it doesn't even require an external device), plug it into a wall, leave it permanently on a TV stand, and plug that laptop to a TV. Doing all that doesn't make that Laptop now a Desktop.
At this point, I think we should just agree to disagree, we have derailed this thread enough.