He is pushing for a political system/values which:
- doubles down on money == power, to a point where only money is power
- uses pretext of "freedom" to remove protections which limit in how much companies can abuse people, mainly in forms which move money from them to the companies.
But if you systematically make it easier to wide spread systematically move money from the demos (populace) to a selected few and make sure only money is power that is pretty clear cut anti-democratic. (I mean it basically remove the demo from democraty).
And sure this is somewhat true for all democratic states, but the question is how much and if you push for it getting worse. Which AFIK Musk does. (It's also why a lot of people which had looked into such power dynamics will look at you strangely when you tell them the US is a beacon of democracy, it isn't and never was. It is a beacon for capitalism combined with wealth, western culture, military might (in some order) and only then democracy. At least in my opinion.)
So what does that have to do with Twitter?
One of the main complains Musk has with it is how it did restrict "freedom of speech", except it mainly did so when that freedom was abused for spread hatred and misinformation, often with the intend to manipulate democracy to elect people pushing for less democracy. And he wants to remove that.
Now without question Twitter did a bad job at moderation, still I would be really surprised if Musk would improve that. I would love being surprised.
Another problem is that Musk has shown to be a petty person and has shown to abuse the power he has over his companies, e.g. to cancel a Tesla pre-order because of someone saying something he took offense with. Putting such a person in charge of a platform like Twitter looks like a recopy for disaster. Especially given that it's also used a lot by some minorities Musk seems to personally have a rather strong dislike for...
Now I would love to be wrong about this assessment. I personally might not be the biggest fan of Musk but what does that matter if he does manage to create a better twitter.
And even if he fails it might have positive effects, by e.g. enabling a better alternative platform to take it's place.