So just like when I first brought up Flying vs. Guarded Conjurations, I will fold to peer pressure like a wuss.
I think you may be handing in the towel a bit prematurely. Given what Shadow says, they do not have a hard rule on this as of yet, so it could go either way. I might not always admit it when arguing my own point of view (afterall I want to appear confident in what I'm saying) but the opposition has made valid arguments. I'm not sure if there's any new information we can provide to Shad0w's call for reasoning, but perhaps it would be a good idea to rehash the arguments.
Below I have listed various positions that I can recall being taken. This is kind of a refinement of one of DeckBuilder's posts. I have tried to fairly present both sides in an unbiased manner. If you feel I have not adequately represented one of the following arguments, please chime in. If you feel there is a position that has been left out, please add that as well. In the arguments below, the Pro position is in favor of revealing your training, while the Con position is against it.
Argument OnePro) Training can affect training restricted spells and it needs to be made clear when such spells are affected. Without this information it is too easy for a player to cheat. There is no other instance in which you are able to keep the legality of something permanently secret throughout the game.
Con) There are currently no spells in the game that are affected by Elemental Training. Even if they were, you wouldn't necessarily have to announce your training until you tried to cast or take control of spell affected by your training. You are able to keep the legality of some things a secret such as the play of hidden enchantments. If your opponent suspects you of cheating, this can be verified with a judge when it occurs.
Argument TwoPro) You must announce your choices in the game. If something gives you a variety of options to choose from at a specific point in time, so that you are unable to change your decision later, you can not keep that information to yourself. Otherwise, how are we to distinguish you making that decision when you were supposed to as opposed to changing it to fit your needs later.
Con) You only have to announce your choices in so far as is required to carry them out. Since your training has no immediate effect, it does not have to be announced up front.
Argument ThreePro) It makes sense thematically. When two powerful mages enter the arena, an announcer would introduce them along with their credentials and accomplishments.
Con) First off, theme does not always directly correlate to rules. Secondly, an announcer would not necessarily reveal everything about your mage. Announcer's in sporting events often listen to the participant for how they want to be introduced.
Argument FourPro) My group currently reveals the Wizard's training (this includes play on OCTGN) and it works fine. We prefer it this way.
Con) My group currently keeps the training a secret and it works fine. We prefer it this way.
Argument FivePro) No other mage gets to conceal their training, and it is unfair for the wizard to get to. It provides them with a significant strategic advantage. If this is intended, then it needs to be taken into consideration with the relative power levels of the mages.
Con) Mages are meant to have different abilities and play styles. The mysterious training is part of the Wizard's. There is nothing unfair about it, although it does indeed need to be considered as a factor when judging the relative power of each mage.