You are completely correct.
Scientific premise: The life of a human being begins at conception, when the union of gametes brings into being a new organism–the embryo–that is both functionally and genetically complete and distinct. The embryo is a living member of the species Homo sapiens–a human being in the earliest stage of his or her natural development. The adult human being whom we know as Joe Biden, for example, is the same human being who, at earlier stages of his development, was a young adult, an adolescent, a child, an infant, a fetus, and an embryo. He developed by a gradual, gapless, and internally-directed process from the embryonic stage into and through the fetal, infant, child, and adolescent stages, and finally into adulthood, with his determinateness, unity, and identity intact. The living member of the human species that is the adult Joe Biden is the same living member of the species who many years ago was the embryonic Joe Biden. For confirmation of these biological facts, the place to look is not the Bible or the Catechism, but rather any modern work of human embryology or developmental biology. The Church holds that the embryo from the beginning is a distinct living member of the human species for the simple reason that it is an established matter of scientific fact.
Moral premise: Every human being possesses inherent dignity, and is equal in fundamental rights; all have an inalienable right to life and to the protection of the laws. No one is superior or inferior to others on account of age, size, location, stage of development or condition of dependency, just as no one is superior or inferior to others on account of race, sex, ethnicity, and the like. Just law, therefore, protects the rights of all, and anyone who supports the withdrawal of legal protection from some bears personal guilt for the grave injustice against them.
The Church has no special revelation pertaining to the scientific premise.
It holds that the moral premise is accessible to human reason on the basis of philosophical reflection, but also finds it confirmed in Scripture (especially Genesis 1:27) and the firm and constant tradition of the Church.
Joe Biden’s idea that the Church teaches that we are required merely “personally” to accept the teaching of the Church against unjust killing of the unborn and observe it in our private lives is absurd. The teaching of the Church is that we are required under strict obligations of justice to support the equal right to life of all. Otherwise, we ourselves stand condemned for injustice towards those whom we would expose to unjust killing. Any way you look at it, Biden is in violation of the teaching of the Church (as he would be if he were to say, “I personally would never kill a Hungarian, since the Church teaches that Hungarians are human beings with an equal right to life; but I favor laws that permit the killing of Hungarians”).
Ryan hit the nail on the head when he said that his position on abortion is based on science and philosophy as well as faith. It is. Biden, by contrast, ignored (or simply doesn’t understand) the science, got the philosophy all wrong, and misrepresented the teaching of the faith he claims as his own.