I'm transferring my Shiny Crobat and Shiny Hoppip from HeartGold to White 2 using Poké Transfer, and it wouldn't let Crobat through because she knew Fly. It won't let any other Pokémon that know HMs through either. IS it a coding issue, or just something nonsensical?
My assumption is that it is because HM moves are not consistent across generations, and 1 or 2 of the moves don't even exist outside the use of the HM. Whirlpool, Rockclimb, and Defog. It's all their fault!
Is there not a Move Deleter in HG/SS? He can save your Crobat!
Also, Pokémon that know HM moves cannot be transferred.
Rest in pizzle Shiny Crobat. HM moves block the transfer.
Source - Bulbapedia
Hope I helped!