Why is Buddhism not Nihilism?
I believe it all comes down to the way one sees reality. One could argue that as everything has been changing since the beginninless time, everything is "Eternal", it is just changing shapes.

I believe the point regarding the middle way is how things exist:

Eternalism suggests things exist as they are. The chair is a chair, it has a "chair-nature", it goes against the dependent origination. Also the name 'chair' is just a convention, nothing more.

Nihilism as we know it is a recent phenomena. The name has a Latin origin, so in the time of the Buddha Nihilism didn't exist like today. It was more related to ascetic practices of thinking that the world is a illusion and nothing exists at all. So the Buddha was trying to explain that things DO exist, but not as we think. There IS a chair, but it does not own a chair-nature. It is something transitory, impermanent with a dependent origination that we perceive with the eye-consciousness