When you read up on U.S. political basics, you can’t help but come across the detail that many of the people in cities in the U.S. seem to lean left, yet what isn’t as clear is why and what influences their concentration in cities/urban areas.
Cities don’t exactly appear to be affordable, and left-leaning folks in the U.S. don’t seem to necessarily be much wealthier than right-leaning folks, so what’s contributed to this situation?
To be fair, the word “liberal” has two meanings. In the US and Canada, the word commonly means “vaguely leftish”, as when people say “the liberal media” or “college makes you liberal”. I think the person you’re responding to is using it this way. This usage is slowly phasing out I think.
The definition you cited is another totally correct usage of the term. It is close to the idea of libertarianism, and is associated with conservative economic policies. So it has the opposite meaning.