Right and left in politics exist because they are fundamentally different ideologies; the centre isn't a new ideology but draws from the other two.
The right stands for hierarchical thinking, small government, deregulation, lower taxes, social conservatism.
The left stands for community thinking, social safety nets, higher taxes, more government involvement.
The left wing system of social housing, trade unions, free to access healthcare & schooling, and a benefits safety net is one way to create a stable society, conservatism is the right wing, and women tend to realise that left wing policies benefit the less well advantaged.
Authoritarianism is an automatic reaction to a perceived threat. Its a survival strategy which can work for a small group dealing with an emergency, but in modern times & complex situations can be maladaptive and create risks; people can be too scared to act independently in a crisis, a society can be so rigid it stagnates, and cannot adapt to change.
The current left is gravitating away from community thinking and towards authoritarianism, and this is happening because purity spirals have replaced analysis and debate.
(A purity spiral is ... a form of groupthink in which it becomes more beneficial to hold certain views than to not hold them, and ... expressing doubt, nuance, or moderation is punished - Wikipedia)
The question is, is this a reaction to a perceived threat, or is it a deliberate strategy of entryism?