How do you persuade them that you’re right or how do you come up with an argument that makes you feel like your chosen ideology does not have any flaws?

The first: you probably can’t. They are just as set in their world view like anyone else arguing on the Internet, including you and me.

Second: accept that all ideologies have flaws. Policies however well meaning have to survive contact with reality first and foremost. Or in this case reality has to survive contact with the policy.