Heres a reason:
After the transfer of keys, you lose the Key the key that you had in one game, hence the term 'transfer' of Keys.
So, if at first, you transferred the Challenge Key from White 2 to Black 2, you lose that particular key in White 2. So when you utilized that key to start the Challenge Mode in Black 2, you use up the Key in that game. So now, after you have done that with the game, you have the Easy Mode Key and White Treehollow Key from White 2. But you don't have the Challenge Mode Key.
The reason is that the game Black 2 is designed to get the Key only when you defeat the Champion again.
EDIT: OK, as per your process then, the last line should be what you need to know. You can't transfer the Challenge Key to Black 2, because the only method if getting it is by re-defeating Iris.
Sorry for going round it so much, just thought it was important.
Hope I helped!