The key phrase was by convincing free users to quit, i.e. the number of paying users remains unchanged but you want to improve the ratio of paying to free. To double the ratio, you have to halve the total (being sure that no paying customers quit).

What helped me understand this is to look at a specific example.

One way to have 99% free users is to have 99 free users and one paid user.

Similarly, a way to have 98% free users is to have 98 free users and two paid users.

But GP didn't say "convert one free user to paid" or "acquire another paid user by other means." The number of paid users isn't changing: you will still only have one paid user.

So you have to cut both numbers in half to keep the same ratio. Instead of 98+2, you end up with 49+1 to have 98% free users.