Most of the time I've seen these situations is when the pilot interviews with two airlines. He's extended a class date at one and is either placed in a pool or hasn't heard back from the second airline. He goes to training at the first and then leaves and goes to the second when he gets the call. The second airline doesn't care about the pilot leaving the first one.

Since most companies allow the pilot to resign before being terminated, anytime someone leaves training prior to completion it is a red-flag. Since we don't know what happened exactly we'll bring you in to talk about it...to find out what happened.

You're going to have to explain it since you must disclose it. (If you received a paycheck from them then there is a paper trail and you must disclose.) It is imperative that you talk frankly about what happened, accepting responsibility and being accountable for your actions. Sure, personal items like Rick pointed out may be a contributing factor, but if there were training problems you have to be accountable for them. It's not the end of the world, but if you try to cover it up, or make excuses, then nobody will be willing to take a risk on hiring you. (Their making a big financial investment here.)
Talk about what you've done since that time to make SURE those mistakes aren't repeated.

People who leave training with "A" airline to attend training with "B" airline also have to talk about why they left (if they go on to interview again with "C" airline.) That can be a sticky situation in itself - - for exactly the same reason - - whether or not the person is worth the financial risk. But instead of being a question of training it is a question of loyalty. So perhaps you've read of people who leave "A" airline to go to their dream airline...the one they plan to retire from? In that case, no explanation would be required...