Ayn Rand rejected Rothbardian Libertarians for 1) his plagiarism; 2) anarchy; 3) the fact that Rothbard joined far socialist party ("New Left".) That is why those quotes above. After Rothbard failed to counter Ayn Rand's criticism of anarchism, bad mouthing was his only option for him and his followers. But let's look what was before.
LETTER TO AYN RAND
"I want you to know that, even without seeing you, you have had an enormous influence upon me—even before the novel came out. When I first became interested in ideas, my first principle that I had from the start was a burning love of human freedom, and a hatred for aggressive violence of man upon man. I always liked economics, and was inclined to theory, but found in my graduate economics courses that I felt all the theories offered were dead wrong, but I could not say why. Mises’s Human Action was the next great influence upon me, because I found in it a great rational system of economics, each interconnected logically, each following, as in Aristotelian philosophy, from a basic and certain axiom: the existence of human beings. When I first met you, many years ago, I was a follower of Mises, but unhappy about his antipathy to natural rights, which I “felt” was true but could not demonstrate. You introduced me to the whole field of natural rights and natural law philosophy, which I did not know existed, and month by month, working on my own as I preferred, I learned and studied the glorious natural rights tradition. I also learned from you about the existence of Aristotelian epistemology, and then I studied that, and came to
adopt it wholeheartedly. So that I owe you a great intellectual debt
for many years, the least of which is introducing me to a tradition of which four years of college and three years of graduate school, to say nothing of other reading, had kept me in ignorance."
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