That's not exactly true - liberalism is basically focused around promoting individual liberties (as the name indicates). In and of itself, it's not really "left-wing" or "right-wing" (in the same way that authoritarianism is usually not considered "naturally" left-wing or right-wing, although there is admittedly debate on that, since some would argue infringing upon the rights of people to determine their own governance is inherently anti-leftist) - but depending on what aspect of society it is actually defending, liberalism can be left-wing or right-wing.

Specifically, economic liberalism is generally right-wing, since it implies deregulation and less government intervention (and thus, weaker public services and disadvantages for the disenfranchised). However, cultural liberalism (and in the US, this would be called "social" liberalism, which confusingly enough tends to be a different thing in the rest of the world) is more associated with left-wing ideas, as it usually opposes conservative social structures.

The US' Democratic Party is (not entirely, but mostly) liberal from both a social, as well as an economic, point of view. In practice, this means that they're generally more to the left compared to the ultra-conservative social positions of the GOP, but they remain right-wing in terms of how they want to organize society, especially economically speaking.