But the network is equally secure whether I own 1 satoshi or 100 bitcoins

So if the value of the currency is derived from the security, why is it value proportional to the number of units I own, which are no more or less secure due to their number?

This is the same root problem with fiat/token money. The $100 Federal Reserve Note is not actually 100x as fine a grade of green cotton as the $1 Note. The relative value of different units is arbitrary.

In contrast specie does not suffer from this problem - 1kg of gold is exactly 1,000x as much gold as 1g, and the material itself is what has value.