I can find nowhere in Scripture where Jesus declares Peter the head of the Apostles. And even we were to interpret some passages to mean that, there absolutely is nothing from Jesus saying that any successor bishops of Rome inherit the position.
And we know that Mary did this...how?
a lack of evidence that any of it actually happened.
No matter what is presented, you will bat it down. The OP asked what Catholics believed. Several Catholics and I answered that.
The questions then turned into "Why?" and "How?" We've answered that.
Now the questions are becoming statements - how we're wrong, there's no proof, etc. There is proof - even that has been given. Lourdes is the place to start.
You're not going to accept any of it, so why bother? This wasn't about Catholics trying to persuade Protestants to believe anything. It was about explaining what we believe and why.
Would you like to start a new thread, entitled: "Catholicism is wrong about all of its major doctrines where they depart from Anglicanism"? Or, I suppose, we could have that debate here.
I will start not with the Bible, but with the most recent miracles and revelations, and the proof that they are revelations (the veridical nature of the miracles). Where you have incredible healings like Christ did, and you have undecayed bodies, you have signs of the divine, which link, going backwards, with previous similar miraculous and preserved signs of the divine, these link back further to more such signs, and they all link back to a particular set of doctrines and beliefs among the many possible about the early Church.
By emphasizing this text and de-emphasizing that text, men can create all sorts of Christianities. God indicated the real one all along by miracles, which he left in permanent form to demonstrate the point for all ages. The first one of these is the Shroud of Turin. The most recent are the medical records of the Lourdes healings.
The healings are real, and are done at a place where Mary appeared, called herself the Immaculate Conception, and after which the girl who saw her there, when she died, wasn't embalmed and did not decay - she can still be looked at today, unrotted.
The nature of the healings include the healings of the blind and paralytics. What power did this, God or Satan?
Can Satan cast out Satan?
Then God. God, at a place identified by an apparition of Mary who called herself the Immaculate Conception. THAT is why you know that the Immaculate Conception is, of all of the different possibilities, the correct answer: it has been revealed by God, by all of the totality of things at Lourdes.
And it just so happens that the totality of things at Lourdes are the sort of things that distinguish the Catholic Church from all of the other Churches - Immaculate Conception of Mary, specific saints doing things in real times that were not agreed upon by ancient Councils. God did it in the here and now, in the Catholic Church. He didn't do it like this anywhere else. This is how Catholics know that ours is the One True Church, and why we are unpersuadable by arguments that don't take things like Lourdes, and Fatima, and Lanciano, and the Incorrupt bodies of Saints into account. These things happened and are real, and we SEE them.
To talk to us, you have to address what WE are looking at, not just flog our old Church book, which is good, but whose narrative stops in the First Century and is thus incomplete.
To simply deny Lourdes is to be a buffoon: these healings are in the 20th Century of people on medical insurance, with medical records. They're very real. To dismiss them as coincidence does not work - there's nowhere else - including the combined total of all of the hospitals in the world, which have a lot more sick people passing through them than Lourdes - where miracles like those happen at all, let alone with that sort of frequency.
What one is left with, then, is committing the unpardonable sin and ascribing the works of the Holy Spirit to Satan.
So instead, all of the physical proofs are just IGNORED. Which means that the Catholic Church and Catholic experience is IGNORED. Which is why Catholics and others have such difficulty talking to each other. We live in a church of miracles. Whatever ignores the miracles is obviously not dealing with the facts or the truth, so what is there to say? Nothing useful.