The idea that these are opposites is, I believe, incorrect.
Anarchy is the ultimate "liberty"-- theoretically anyone can do anything, but practically, it sucks.
In reality you'd end up with less overall freedom/liberty, because you'd have to spend most of your time ensuring you don't die, your stuff isn't stolen, etc. As a result, you can't support nearly as much specialization (farmers can't just be farmers, they have to be farmers AND warriors to protect themselves), which means everything is less efficient/productive, and you end up with a lower quality of life, more death/starvation, and worse stuff overall.
The truth is that practical freedom/liberty comes from providing sufficient stability that specialization can happen, that not everyone has to be a warrior, and that you and the things in which you've invested time/effort are reasonable secure from being take from you.
If freedom is measured as being able to do things that you want a maximal %age of the time, then, by that metric, we must give up /some/ freedoms in order to get time with which to do the other things you'd want.
If anarchy is one end of the spectrum, then authoritarianism is one of those things at the other end. Authoritarianism also reduces your ability to do what you want a maximal %age of the time.
The "best" area is in the middle between these.