I tend to think part of the problem is there are potentially a huge number of apocrypha books.
Writing was not uncommon at that time and huge numbers of texts of every subject imaginable would have been produced.
There would also have been many people called Peter, writing stories about aliens, traveling to the other side of the galaxy to battle whatever and finding a planet entirely inhabited by some 1920s version of Chacago. But sadly, such were simply not considered relevant enough for inclusion in the Bible.
The four Gospels, for example, were included, because there was a substantial amount of evidence to show they had originated from reasonably reliable sources. What the modern TV cop show might call, Chain of Evidence. The same mention of verification is also use by scholars of Islam.
Sadly, for the proponents of the Bible, Islam, not to mention the huge number of innocent people convicted, the method is not as reliable as it seems.
The approach is actually part of the academic process, starting from a given source, usually one that is generally accepted as reliable, then working forward, in reliable steps. Equally, starting form where you are and working back to the source, accepting that each step, having been verified, will be reliable.
It fails firstly because what is judged to be reliable is a matter of opinion. Because something sounds right or is generally accepted, is not the same as being right. Hell, for example, clearly is a preposterous notion. The more we look at it, the less reliable and less credable it becomes. Yet to say that to most Christians almost invariable results in some snooty dismissal followed by a visit from the local 9 95 god botherer.
So, basically, the reason some books are deemed Apocrypha is not part of a general conspiracy by those nasty anit-christ popes. It's because they are obvious nonsense written by numerous people in ancient and not so ancient times, to entertain or simply, in the case of Paul, to describe the effect of being utterly insane.