"We believe that liberty for all requires members of society to forfeit some freedom". Is this proof that liberals don't understand liberty?

If you want unlimited individual liberty, fortunately for you there are places where that exists.  Those places are called "desert islands".  You can move there and enjoy all the individual liberty you want until the end of your days.

If, on the other hand, you want to live in a society, individual liberties are going to overlap and come into conflict.  That's why individual rights have to be regulated, in order for the society to continue to function.

This is not a mystery.  It's how societies work.  Always has been.

Clearly you don't. No rights are absolute as they would inherently conflict.

I think Americans feel they can marry whoever they want and have or not have babies.

Just that your reading comprehension needs some work. But don't feel bad. At least you can read!

Everyone knows that quotation marks make it true.

Whom are you quoting, dear, and what's the precise source of the quotation?

In my classes, people get low grades for failing to provide proper citations. Did you even graduate from high school?

You also need to learn what "proof" is.