Catholics first must believe all that the Church has defined as "de fide" (of the Faith). These are all of the dogmatic proclamations and solemn decrees of Popes and Councils, which very few would argue with. The difficulty comes with the ordinary magisterial teachings of the Church; traditional teachings of the Father's and Doctor's of the Church, also known as Catholic doctrine. These are the common teachings of the Church which She has not found necessary to solemnly proclaim. But by the fact that they are universally taught they are also infallible. To these as Catholics we must also submit. Vatican II Modernism falsely teaches that we may dissent from these, in a blatant contradiction of Vatican I.
Why must we believe these things? Because it is the Will of God for man that they show their love by keeping His Commandments. God has deigned that men learn of this through His Church when he said to his Apostles: "teach ye all nations" and "he that heareth you, heareth me". Only those who are enemies of God can refuse His Will. Catholics are rightfully those that seek to do God's Will as revealed by His Church.