Instead, suppose you try to convince people of the similarity between government and organized crime. You say that both provide “protection” backed by coercion. The advantage of this is that if you can get someone to shift to looking at issues along the freedom-coercion axis, that person will be less receptive across the board to arguments for state intervention based on the oppressor-oppressed axis or the civilization-barbarian axis.
Just a reminder that minarchy is coercive. Libertarian government will coerce me if I try to tort you, rob you, break our contract, tack a nap in your bed, walk through your yard, whatever.
The scale of coercion isn't even necessarily smaller in a libertarian state. You could imagine a state where social norms are breaking down -- maybe there is a bad recession or a war of self defense or a disruptive technological change afoot -- and *lots* of people *really* want to steal or break and enter or tort or assault. The threat or use of force is actually having to be invoked super often to change people's behavior. Just so, you can imagine (and might be living in) a state where most people don't particularly mind paying their taxes, and the threat of and actual use of force is less necessary to get them to comply with tax law than it is to get our people in the first state to respect property law. Even more important, you can imagine (though it may be unlikely) taxation and redistribution transforming the first state into the second state -- maybe the state taxes people and subsidizes public education, giving people a road out of poverty and, over time, making the masses less grumpy. Maybe it's a social insurance program. Whatevs. Point is I can imagine a welfare state ultimately coercing less than a libertarian state would, with coercion defined as using force or the threat of force to change behavior.
Now you may think it is extremely unlikely that welfare-state policies will have that outcome, but that's an empirical and economics question more than it is a philosophical one. To the extent it is true based on empirical observation that libertarian states coerce less, we are making a pragmatic or consequentialist argument, not an ex-ante ideological argument. And pragmatic libertarians are all right in my book.
Which isn't to say ideological libertarians are clearly wrong. Ideological libertarians like minarchy because they think it coerces for the morally right reasons, IE to enforce the harm principle. But they should argue that. This whole "its all about coercion vs. freedom" thing is either a wrong or a pragmatic argument, it isn't a self evident philosophical truth. The argument they want to make is "it is about justified coercion vs. unjustified coercion." The state isn't the mafia because it is possible for the state to coerce you for justified reasons, but it *can* *be* like the mafia if it goes too far.