Let's try this from another angle...
Let's say I write a letter to my sister. In that letter I say "I was one foot out the door when I realized I forgot to call you". Two thousand years later, some archaeologist digs up my letter. Do you think he could correctly interpret my comment? Did I mean I was exactly 12 inches on the other side of the threshold? Did I mean I was straddling the threshold? Or did I simply mean I was in the hurried process of leaving? The text alone cannot solve the dilemma.
My sister loved me so much, that she made copies of my letters and gave them to her children. She told each of them the stories behind my letters and what all my funny little sayings really meant. She instructed her children to hand this information, both letter and interpretation, down to their own children. In doing so, she started a tradition. Her children and grandchildren, being faithful to her request, have kept the meaning of the letters intact.
If the archaeologist were smart, he'd check with my sister's great grandkids before racking his brain too hard.
Yes, but I think it's a weak analogy. For one thing, the content of letters to your sister is never going to be an issue of great cultural and political importance, whereas there is actually an incentive to twist Scripture as religion has been used to control people for centuries.
Secondly, passing this tradition down is like game of 'telephone', where the content can evolve with each generation of hearing & re-telling. If it gets to the point where your great-great nieces and nephews have interpretations that contradict the text of your letters, then I cannot count on them as reliable sources. Especially if, in your letters, you predict that people are in later years going to claim to be your relatives and misrepresent your letters.
Thirdly, I feel confident that God is a better writer than you or me, and can make Himself understood without needing a lot of help from flawed human beings.
Point being, there is something in the Protestant approach that boosts this dividing ratio tremendously. I think the root cause is ostensibly Sola Scriptura.
The Bible is simply not that badly written. An honest appeal to it cannot support scores of mutually exclusive doctrines.
As far as why this division is so much more prevalent in Protestantism, I imagine it has a lot to do with the authoritative hierarchy of the Catholic church, and the fear of members that they would be lost if they left it. Lots of protestant denominations have developed hierarchies of their own, but the false doctrines of salvation by faith only, once-saved-always-saved, etc., have created a mindset among many that they can choose whichever church they like, or even start their own, and everything will be just dandy. And again, these doctrines -- being false -- cannot originate from an honest, thorough examination of Scripture.
By the way, there were certainly divisions already taking place in the first century -- churches and individual Christians were admonished by the New Testament writers for their partisan tendencies ("I am of Paul" "I am of Apollos") and for drifting away from sound doctrine. Entire congregations -- i.e., Laodicea -- had seemingly gone into apostasy. Were they Protestants?
BTW, I do not consider myself a Protestant, though I imagine you certainly would.