Rothbard was talking about the "could" and not about the "should"

Which is exactly what the other person said: "Some libertarians support baby markets and the ability of parents to let their children starve to death because they take the logic of it being the worst moral wrong to aggress upon someone, something not permissible unless someone aggresses on another, no matter what."

Now why is that a straw man? Because, he was objectively not talking about the reality of the situation; which you portrayed as what our ideals would be like.

Nope. You're the one engaged in strawman here, by claiming that the poster is making a statement about libertarian ideals rather than libertarian abilities in order to make his actual claim easier to refute.

When libertarians advocate that bakers should have the ability to refuse service to gay people, then it means exactly that. I don't need to prove that libertarians want gay people to be discriminated against to make my point, I simply need to prove that they want bakers to have that ability. The same goes with giving coal producers the ability to inflict climate change, or giving anti-vaxxers the ability to deny vaccines for their kids.

All you have to do is apply morality and reasonablity to that text.

"All you have to do is pretend that people will never abuse their liberty to do bad things, and then giving everyone absolute liberty makes perfect sense."