Can't go from authoritarian to Egalitarian

[Kleiner's final Form]

I literally can't, theres no faction forming around it and I can't raise the living standards beyond social welfare because I'm authoritarian. What do I do?

[Oakshadow]

There's a couple things.... first definitely go social welfare. Not using stratified society will help.

Abolish slavery in policies for species that aren't your default.

Allow for free movement (abolish forced relocation) and ban any form of population controls.

look for an egalitarian neighbor and invite them to a migration treaty (assuming you share similar enough climate preferences)

Basically you want to lean your policies as close to what is standard for egalitarian empires as possible. While letting foreign pops that might lean more egalitarian into your empire.

If you need further help, holding your mouse over the egalitarian ethic dot along the top of the factions screen will show you what's pulling and detracting from the ethic. You can use that as a guide to better aligning your empire so that the faction might show up.

Keep in mind it can be rather difficult to switch ethics from heavy spiritualist and authoritarian empires as both get governing ethics attraction bonuses. so you have to go hard for it if you really want to change things up.

Edit: almost forgot. You can help to open up your ethics by doubling down on other ethics you currently have. By getting rid of authoritarian as a governing ethic Egalitarian will be more likely to show up. To do this discourage authoritarian ethics. And promote one of your other factions. Once authoritarian support is the lowest between your other ethics, embrace the promoted faction.
Mind you if you have fanatic authoritarian, even if it has the lowest support you will only lower it down to normal authoritarian. I recommend doing this with an ethic you don't already have.
Xenophilia is a good co-ethic to egalitarian as the two frequently generate support for the other. So if you don't have egalitarian embracing that should help egalitarian show up.

edit:2
I also forgot to mention. though I could be wrong about this one. if your authoritarian ethic isn't fanatical, you should be able to reform your government to be oligarchical. This government type is in between democracy and dictatorial. So that too should help loosen things up a bit. I don't typically play normal empires though, so I could be wrong about oligarchy being available to authoritarian empires.

[Mennan]

Another way to change your authority is to find a Democratic crusader or other empire that allows ideological wars. They almost always have their #1 war goal as ideological war. so just declare war on them check their war goals and if it is IMPOSE IDEOLOGY and you want to their government type to be yours just auto accept surrender, this will then make your their authority type Afterwards you can just reform your government to re-select your prefered civic slots