I leveled my Cleffa up to lvl 80 without evolving. Clefairy is supposed to learn Moonblast at level 46, but since Cleffa wasn't evolved, she never learned Moonblast. I went to the Move Relearner for my Clefairy to learn Moonblast, but wasn't provided the option of Moonblast. Instead, it gave me Cleffa's starter move options. 

Sometimes the move relearner doesnt show you all the moves on the first time talking to it. Try to interact with the Relearner NPC again and you should see more moves.

However on that case you would have to use the Pre-Evolution-Tutor in the daycares to teach Moonblast if I remember correctly.

Hello @smokyjasmine. Apologies for the inconvenience. 
 

As Norex mentioned, sometimes the Move Relearner does not show all the moves a Pokémon can relearn. Could you try selecting a move and seeing if the rest become visible? Or re-interact with the NPC.

If neither of those work, please let me know. 

Thank you so much for your quick input. Selecting a move worked for me. 

Glad to see your issue was resolved. I will now lock this thread.

If you have further questions or another issue, don't hesitate to make another thread.