What you are missing is that Americans a very against centralized anything, they want everything to be local, and then flow upward from there.
In general Republicans are more against central control, and Democrats more for it (but not as much as Europeans).
So for example that voting rights fight going on right now is not about voting rights, it's about the Federal government setting rules (Republicans are against that) vs. the State setting rules (Democrats are against that).
There's arguments both ways for which is better, I don't want to go into that, but this should help explain what you are missing.
This same argument shapes things like Health care - which is currently local, not federal, and actually a HUGE amount of political stuff boils down to local vs federal.
Another thing is that personal determination is equated with local control (i.e. person decides what's best for themselves), while federal control is equated with social services (since some central authority decides what services to render).
Keep in mind the way the country was created was "united states", with the main authority being the state, and the federal government given only limited power. Also keep in mind a US state is similar in size to a European country.