Freudian slip.
Why equate liberalism with conservatism? Conservatism wants to preserve existing structures and norms. In cases where those structures and norms are liberal, then conservatism will be very similar to liberalism. But in cases like Germany, where the old status quo was nationalist and authoritarian, it's not surprising that many conservatives would support illiberal parties.
I don't think it's fair to classify fascism as either left wing or right wing. After all, it was meant to be the "third way". It was right wing socially, while generally left wing economically, traits that are shared by most nationalist parties today.