"doing that is increasing the supply of bitcoin units"; I think it's debatable exactly what that means with the word "units" at the end, but it is not debatable that without it, the sentence is flat out wrong. A building doesn't become taller when you measure it in centimeters instead of meters. There is no such thing as "a bitcoin", or "a satoshi". Any more than there is "an inch". It's a measuring unit. You can change measuring units if you like, for all kinds of reasons, but that doesn't change the thing you measure.

Bitcoin units are those 2,099,999,997,690,000 things that the software creates and verifies the movement of. It's not a unit of measurement.

It's not a big deal IMO. The point is that the network cannot be DEBASED, which is increasing the supply unfairly. Simple increasing further division of the current network total value by adding a few zeros to every user's balance, and thus increasing the total units, every few years is not unfairly affecting anyone and only enhances usability as the value of each satoshi rises. Also, we can even just keep the total network division as "21M" by leaving the software placed decimal at 1 / 21M of the total. This debate is only controversial when a Satoshi is still a penny or less. Once a Satoshi becomes worth $1 (~2035~), $10 (~2038~), $100 (~2041~), and so on there will be no debate and consensus will be found to update Bitcoin. Allowing further division as Satoshi himself considered a possibility.