Something that worked for you won't necessarily work for everyone. Yeah, you have to challenge people's ideology, but you you also have to maintain credibility with them. If someone challenges your ideology but lacks credibility you write them off as a crank.

We're talking to people who are skeptical to oppositional. With those people, you can't give them an inch to argue or they'll pounce on it so they can avoid the harder issues you present to them. You want to talk about things where there is as little room for debate as possible, even among libs.