Good question. This is a common claim of Roman Catholic apologists, but it's a bad argument.
Their argument is that their church decided the canon, so if we trust the canon, we should trust their church. However, that's simply not what happened.
For their argument to work, the canon would need to have been decided by a decision by the institutional church, like an ecumenical church council. If that were true, then we would need to trust that church council if we trust the canon. But that's not how the canon was decided.
Instead, the canon was decided a very different way. The church recognized the writings of apostles and companions of the apostles as authoritative. There was a unanimous consensus from the very beginning on the authorship (and therefore authority) of most of the books now found in the NT. So even if we didn't follow anything other than the unanimous consensus of the pre-Nicene writings, we'd still have a canon of 20 or so of the books that we now have.
So the question is about the seven books that weren't unanimously affirmed. These are often called the "disputed" books, not because anyone saw them as bad, but because not everyone was absolutely sure that their authors were apostles or companions of the apostles. Over the course of the fourth century, without any ecumenical council, church leaders from all over the Christian world came to a consensus that the "disputed" books as apostolic as well.
So where does this support the idea that the Roman Catholic Church has authority over the Bible? Nowhere. The canon was decided based on who wrote the books, not based on a church decision. It wasn't decided at any official church function, but the issue simply settled itself through the majority of the Christian world coming to a natural consensus.
For more information, I have an article that lays all this out in more detail.
Excellent point(s) Lynn
I've been studying this topic lately as well, and would like to chime in if only to keep the conversation going.
I would add that what helped me understand the cannon was to understand each individual book, and it's position to the church universal.
For example, the book of Hebrews' author is debated, but the content of the book is not brought into question by any early church father.
In other words, there was never any question if the content was inspired by The Holy Ghost. (someone correct me if I'm wrong)
So that shows us that the early church didn't so much require who wrote the book, so much as if the content was Inspired and if the tradition of the church kept the book regarded as Scripture over time.
An example of a book that was highly regarded, but not acknowledged as Scripture is the book of 1st Clement.
If what I'm saying is accurate, then Church counsels don't so much determine The Canon as record and acknowledge what the Holy Ghost has lead the Church Universal to already decide is Canon.
I personally think the Catholic position is much more solid than the original reply. Having said that, it is not something that can be so quickly sorted out in an online discussion. Aside from countless Catholic sources giving their position of how we got the canon, for example Catholic Answers would most certainly have articles and books in depth on the subject. The best non-Catholic book I have read on the subject is called 'Canon Revisited' by Michael Kruger.
You might find that an interesting read as I did. God Bless.
I'm definitely not trying to say that Catholics can't think about the canon in a good way. I think they can.
I just think that the argument of apologists, as I've heard it, has been hard to square with the history of what happened with the canon. Those who are more aware of the history, of course, wouldn't make the argument in the way described above.
Also, overall, I don't think any tradition can make a good argument that the way the canon was decided is evidence for their church's authority.
I hope this clarifies my intent.