It's explained pretty well in the article. Basically with CTR using the block # as the nonce you break the security assumptions of a nonce (use only once). If the cryptofunc is static, and you are editing a document in place, an attacker can see exactly which bytes changed and do other statistical attacks.

Think about a file that you preallocate with NULLs. If you get an image of the disk before you write to the file and then an image once you write to the file, you can simply XOR the before and after to get the ciphertext.

e.g.

  using block 100
  cipherblock_before = cryptofunc(100) ^ 0x00 = cryptofunc(100)
  cipherblock_after = cryptofunc(100) ^ data
  cipherblock_after ^ cipherblock_before = data