Left = Egalitarian flat power structure https://en.wikipedia.org/wiki/Left-wing_politics
Right = Hierarchical power structure https://en.m.wikipedia.org/wiki/Right-wing_politics
The collectivist/individualist framework you describe is propaganda to appeal to supporters.
Authoritarianism is the sole perview of the right. What makes it confusing is that right wing people claim to support leftist ideals.





In addition the founders of Israel broke the international Anti-Nazi boycott to build their right wing ethnostate. This is who they have always been. Their support of the Nazis directly contributed to the holocaust.
https://en.m.wikipedia.org/wiki/Haavara_Agreement