Why does RAID 6 require at least 4 disks?

The reasons AFAIK is just performance. There is no real technical reason against it.

There is a difference between a 3-disk raid-1 and a 3-disk raid-6.
The redundancy calculations for raid-6 are computationally harder and more complex than for raid-1.
Therefore using a 3-disk raid-6 requires far more horsepower from the controller (hardware) or CPU (software-raid).
Rebuilds, if needed, are also more time-consuming.

It is therefore pretty pointless to do raid-6 on 3 disks when raid-1 gives the same level of redundancy with less performance issues.

As a result the option for a 3-disk raid-6 is usually not even made available by the programmers of the management software of the raid.

(If I remember correctly I have seen a Raid controller some years ago that allowed it. I can't recall the brand/model but it almost had to be an Areca controller or one of the HP/Compaq Proliant controllers. We were dealing almost exclusively with those at the time.)

It requires 4 drives because RAID 6 has block-level striping with double distributed parity. This allows for the failure of 2 drives. You cant do this with less than 4 drives and keep the required redundancy.