Society is already highly unstable due to "herd mentality" and conformity to dynamic and evolving nature of human culture, values, and morality. Just look at the insanity and instability of 2020 for example.

Nietzsche's point is to break free from societal constraints, think independently, and create your own values.

Societal norms change constantly and quickly which is why he said:

"No shepherd and one herd! Everybody wants the same, everybody is the same: whoever feels different goes voluntarily into a madhouse."

"In individuals, insanity is rare; but in groups, parties, nations and epochs, it is the rule."