It's not clear just from this screenshot, but Freedom of Assembly is a law in the Free Speech category of Laws, which "culminates" in Protected Speech. As the most liberal Law in this category, it grants no Authority, while more repressive Laws (like Freedom of Assembly) do. In isolation from the rest of the game, of course that means it looks like granting your people rights increases your Authority but that is actually the opposite of what is happening.
Also, this is of course not the only thing Free Speech Laws govern, there are other effects of the Laws as well which provide trade-offs to your country, but this is the only effect it has on Authority.
The reason why Road Maintenance uses Authority is because it's a decree (one of many different types) issued in a state to its population, and doesn't cost the government anything other than the Authority to ensure its people are following its directives. This is a pretty early-game solution to maintaining a good market connections in a few states at a time, more effective means of leveraging your economy to ensure cohesion between your states tend to emerge later in the game, freeing your Authority up for other things like suppressing your political opponents (or, you know, granting your people more rights, if that's how you want to go about it.)