You gotta love the Duke.
Its confusing as hell, its wrong, and yet at a certain level he's right.
Confusing, well obviously. I mean who works things out like the above. Actuaries perhaps, but they already understand what is happening. It a good job accountants are not so cavalier, because the rounding error in the above example mistakenly leads him to conclude that no tax is due whereas there is a small liability if you sell €25,400 of shares.
He is wrong because 1.6% of €1,575,000 is €25,200 and not €25,400
He is right because
You sold shares for €25,200. (not €25,400)
They cost you €24,000
So you made a profit €1,200 so no Capital Gains Tax due.
The remaining shares will be subject to CGT if and when you sell them.