You should agree with them on this point. "Liberal" is rooted in the word "liberty", and most "progressive" issues have nothing to do with liberty.
Speech codes (you can't say what you want). Gun control (you can't own a gun). Taxation (you can't keep what you make). Single-payer health care (you can't choose your own health care). Social Security (you can't use your own money to provide for your own retirement). Public education (you can't use your own money to provide for your child's education).
Nothing approaching "liberty" in any of that.
Some good points and worth taking note of for future conversations.