Here, it appears as though you are eagerly attempting the very thing that Rome says we are not competent to do on our own–interpret the bible. And on your interpretation, only that which is visible can last and have continuity.
Rome, or more properly, The Vatican - I suppose, has a very limited number of bits of Scripture to which it attaches an intrepretation beyond question. Suggest you research how many bits exactly…its interesting.
Here is the Bible bit that you’re worried about:
There is no super-duper interpretation needed in this following sentence, it simply is what it is:
“…and upon this rock I will build my church, and the gates of hell shall not prevail against
it.”
The ‘it’ bit I underlined because the ‘it’ He refers to can only be a Thing.
The constituent bits that make up the Thing
are visible people, namely the visible hand-picked Apostles, then the disciples, then the ordinary Catholic faithfull. The other bits that help complete this Thing are;
The Holy Spirit living in this Church; He said therefore to them again: Peace be to you. As the Father hath sent me, I also send you. When he had said this, he breathed on them; and he said to them: Receive ye the Holy Ghost.;]
Unity of Doctrine, All the Apostles, disciples, and laity believed the very same things; [Therefore, brethren, stand fast; and hold the traditions which you have learned, whether by word, or by our epistle.]
A Unified Organization of people: [For the promise is to you, and to your children, and to all that are far off, whomsoever the Lord our God shall call.]
To deliver this same Promise as St. Peter says, to every place in every time, and as prophecied - until the end of time, there needed to be some organization to protect Doctrine, otherwise you would be subjected to a protestant-style chaos - resulting in the type of confusion you are experiencing now.
The great thing about Catholicism is that because of the foresight of its Founder and Fathers, anyone can without any trouble compare the Doctrines of Catholicism today with Catholicism at any date in the last 2000 years, - it is recorded history. So you are sure, beyond any doubt, that here at least is a true record of Christianity from the beginning and its promise.