When debating Catholic doctrine, Catholics will often appeal to post-Biblical, pre-Reformation history. The header image closely mirrors many discussions I have had with Catholics, and I've never had a full debate with a Catholic wherein tradition is not referenced as if their authority is indisputable. Some Catholics have even lamented that I don't accept the word of one of their Councils as proof of their doctrines.
But why is it always post-Biblical history that is appealed to? It's never even anything written in the first century, it's always second century or later. As I always say, Catholics appeal to the early sources because they cannot appeal to the first Christian source.
In various places throughout scripture, we are told that the Bible is the ultimate authority for all things Christian. Most specifically, 2 Timothy 3:15-17 tells us it gives us everything we need to be complete men of God and thoroughly equipped for every good work. In other words, if something isn't in the Bible, it isn't Christian.
But of course, a lot of Catholic doctrine developed after the Bible was written. The Apostles were long dead before there ever was a Pope. Mary would vomit if she could see the near-divine status the Catholic Church has ascribed to her today. Peter utterly refused to eat any unclean or common animal at the direct command of God, so no doubt he would have had a thing or two to say about transubstantiation. Purgatory still belonged to the pagans when John wrote Revelation. The Catholic Church cannot appeal to the Bible for its most unique doctrines because the Catholic Church simply didn't exist at the time.
One of the things both Christians and Catholics agree on (in theory) is that the Bible is the inspired and inerrant word of God. Therefore, as a Christian, I want to believe every word that is found within. If a Catholic doctrine can be found within the Bible, it won't take much to convince me. This is shown by the number of common beliefs Christians and Catholics hold. We agree on the Trinity, we used to agree on creation in 6 days (that's a little shaky now), we agree on the sanctity of marriage, the value of human life, things like that can all be found in the Bible, and thus Christians believe them, not because of a Council, or a Church "Father", or a Church, we hold these common beliefs because the Catholic Church happens to agree with the Bible on those things.
But I reiterate, the reason the Catholic Church cannot appeal to the Bible in this same manner regarding things we disagree on is because their religion isn't in the Bible. And that wouldn't be so bad; Christmas isn't in the Bible either, yet only a few very grumpy Christians think Christmas is sinful. But Catholic traditions often go beyond a season of fun to brighten up the dark winter. Many of them are the antithesis of the Gospel itself. Catholic tradition and scripture aren't just separate in that the Bible does not mention them, but in that the Bible actively opposes many of them.
The fact that Catholics cannot defend their views without appealing to tradition is a huge weakness for their wonky theology. An inability to stick to the Bible is a strong evidence that your faith is not Biblical. As a Christian, I don't hold many views that I can't defend Biblically. The views I do hold that I can't defend Biblically, you will rarely, if ever, hear me profess. If Catholics had the same attitude, you would never hear of Catholicism.