I believe one reason statists aren't receptive to liberty is that, while it is offered as a "fix things" suggestion, they take it as a "fix YOU" command.
Advice on how to fix things is usually appreciated. You are trying to replace a defective whatchamacallit on your widget, and you're stuck. Online videos haven't helped. So, you reach out and people offer suggestions on how to fix it. Either it works, or it doesn't. It's either within your ability, or you know to pay a more experienced person to do it for you.
But, when things are messed up in your life, most of the advice isn't that helpful, even when well-meaning. Unlike a widget- the exact specs of which are known, or accessible, to many- there are circumstances about your life you haven't made public. What works for one person in a different situation may be impossible for you to do under your individual circumstances.
I think this is one difference in how statists see libertarian solutions.
We know the solutions will work if put into play. Repecting liberty always works. We are offering advice on how to fix a broken widget (a system).
Statists believe we are telling them how to fix themselves.
Sometimes this is because they are so invested in the broken widget that they feel it is a part of themselves. They want a government to work because they identify with it. "Our country", "my president", "our government", and other not-so-subtle hints will expose this feeling they have.
It's hard to get someone like this to admit there's a deeper problem than just having the wrong politicians in power today. They feel like you're telling them there's a problem with themselves.
Thank you for reading.
