Why do 1st and 3rd key have to be the same in 2 key 3DES? From this answer:


  However, that wasn't the only situation they had in mind; they also
  considered the case where someone implemented 2 key 3DES in hardware
  (which the first and last subkeys were constrained to be the same)


Why are the first and last keys constrained to be the same?
In two key 3DES two keys are equal so that key size is only 112 bits, compared to the 168 bits of full 3DES. The advantage is a smaller key size without a correspondingly large loss in security: both two and three key 3DES can be attacked in about $2^{112}$ time.

With the encrypt-decrypt-encrypt construction it clearly must be the first and last key that are equal, since having two adjacent keys equal would make the decryption and encryption cancel out. Even with EEE it would have been weak to have equal keys adjacent: it would effectively be a cascade of two 56-bit strength ciphers (DES and double-DES), which a standard meet-in-the-middle attack breaks in roughly $2^{56}$ time.

So having the first and last keys equal is the only option that makes sense.