The Jesuit magazine America tackles Paul Ryan's 2005 speech at the Atlas Society’s "Celebration of Ayn Rand" (there's no video – but there is audio). America's Vincent Miller explains how the philosophy Ryan believes in is so inimical to Catholic thought and tradition:
In the published transcript Ryan states that like Rand, he views all political and policy questions as battle between individualism and collectivism.
(2:38) In almost every fight we are involved in here, on Capitol Hill, whether it’s an amendment vote that I’ll take later on this afternoon, or a big piece of policy we’re putting through our Ways and Means Committee, it is a fight that usually comes down to one conflict: individualism vs. collectivism.
This philosophy leaves no room for Catholic notions of Government in service to the common good, there is no room for a social conception of the human person. Rejection of Rand’s atheism notwithstanding, Ryan’s policies are based on a political philosophy completely at odds with the principles of Catholic Social Doctrine. "Prudence" is an insufficient measure of his proposals and the threat this philosophy poses to the Catholic faithful.
Ryan is more hostile to the core social teaching of Catholicism than Obama could ever be.