Why can't we use the IDEA's decryption rule for decrypting a block on CTR mode? Suppose that a block is ciphered with IDEA using CTR mode operation. To get 
 the original message, why can't we use the cyphered rule?
CTR uses only a block cipher's forward algorithm, not its inverse. Both sender and recipient compute $N_? = E_K(nonce || counter)$ for each block. Then the plaintext is XORed with $N$ to get ciphertext. The recipient XORs ciphertext with $N$ to get plaintext.

$C_i = E_K(nonce || i) \oplus P_i$

$P_i = E_K(nonce || i) \oplus C_i$

Note: XOR is it's own inverse. $A \oplus B \oplus B = A$