"There exists a private hospital in a country of superior quality to a public hospital in the same country" is a weak claim. Even weaker is "there exists a private hospital in the world of superior quality to a public hospital also in the world".

Private hospitals are usually nicer than public ones everywhere, but that's obviously to be expected.

However, that misses the point of state involvement in education and healthcare, which is universal access. Of course people with money will have access to (good) schools and (good) healthcare. The state is involved so that everyone has access to those services.

Education and healthcare also have network effects. If people near you are ill then you're likely to also become ill. If people around you think taxation is theft and coercion then they can band together and elect people with similar brain worms into government.

I'm fairly certain that the claim you're replying to is that private hospitals in the countries in question are consistently better than public ones.

If that was the claim, then why consider African hospitals instead of any hospital?

because:

1. its were I live

2. its where glib statements about the virtues government-run organisations slam into cold hard reality. More so than say Switzerland.

3. try get an EU/US/CA/AU/NZ/JP expat to work in Africa and expect his family to use government hospitals. Really, try.

Because those are the countries in question.