Why do you think he was reactionary?

Probably because he was. The easiest thing to point to is that he was a devout anticommunist on the basis not only of disdain for the specific communist movements of his day but because he thought the stated goals of communism, e.g. "to each according to their need," an end to war, etc. would effectively mean the death of the human spirit. He gets sanitized all the time but he was fundamentally loudly opposed to social progress except for his own schema of an atomized second "revaluation of all values" to have the non-sheeple live as moral artists and inventors.