"Why do Christians accuse atheists of misreading the bible, when Christianity has split into thousands of sects because they can't agree on the correct interpretation?"
Well, you have to take in account that there used to be no room for interpretation. It helps if you understand that. Then there's the Russian and Greek Orthodoxy that differ from the Catholics.
All the way up until Martin Luther nailing a pamphlet on the church door.
But even more compelling is this quote from Thomas Paine.
Let me introduce you to the words of a man named Thomas Paine:
It has been the practice of all Christian commentators on the Bible, and of all Christian priests and preachers, to impose the Bible on the world as a mass of truth and as the word of God; they have disputed and wrangled, and anathematized each other about the supposed meaning of particular parts and passages therein; one has said and insisted that such a passage meant such a thing; another that it meant directly the contrary; and a third, that it meant neither one nor the other, but something different from both; and this they call understanding the Bible.Now, please, buy a T-shirt
It has happened that all the answers which I have seen to the former part of the “Age of Reason” have been written by priests; and these pious men, like their predecessors, contend and wrangle, and pretend to understand the Bible; each understands it differently, but each understands it best; and they have agreed in nothing but in telling their readers that Thomas Paine understands it not.
-The Age of Reason Part II published 1795