To simplify, the faith is the WHAT believed while the rule is related to the WHY believed.
What do I believe? the Assumption. Why do I believe it? Because it was proposed as dogma by the authority of the teaching Church (proximately) and ultimately by God in revealing Himself (remotely). So it's the proposal by the Church (viewed formally) that's the rule of what I believe.
This is similar to the distinction between the faith itself (the contents of Revelation) and the faith viewed as supernatural virtue as moved by the formal MOTIVE of faith
Like Ockham’s razor, this is very neat oversimplification trying drive a wedge between necessary elements of the virtue of faith.
If the Rule of Faith only answered
why we believe, then Scripture and Tradition, the remote rule of faith, would have nothing to say to the question of
what. This is obviously mindless proposal.
But, since faith is believing what God has revealed on the authority of God (why), the revealer, the rule of faith necessarily answers both the questions, why and what. What a Catholic believes and
why a Catholic believes it are both attributes of the virtue of Faith. If you drive a wedge between these attributes, the faith is lost. The rule of faith must necessarily address both questions and it does so in both the remote and proximate rules.
When the pope employing the teaching office of the Church engages the Church’s attribute of infallibility it is affirmed that God is the revealer answering both the questions of
what and
why. Such as in Vatican I
Pastor Aeternus, on papal infallibility: “Therefore,
faithfully adhering to the tradition received from the beginning of the Christian faith, for the glory of God Our Savior, the exaltation of the Catholic Religion, and the salvation of Christian people, the Sacred Council approving,
We teach and define that it is a divinely-revealed dogma…”. Your oversimplification makes the pope the revealer. The pope is the necessary but insufficient material and efficient cause of Dogma. God is the formal and final cause. Dogma is the proximate rule of faith.
Drew