Trial is fundamentally a credibility fight. The more credible side wins. If your lawyer isn't armed with the whole truth about your case, there's a chance your lawyer could be blindsided by the defense bringing to light the bad or embarrassing fact.
The fact is, if your lawyer had known about the bad or embarrassing fact, your lawyer could have dealt with it in a favorable way before trial. However, once the jury realizes that your lawyer didn't know your whole story, you lose credibility with the jury, and it can cost you the case.
No matter how scared you are of the fact, you have to tell your lawyer the whole story about your case. Your lawyer is on your side through-and-through, and he or she isn't going to judge you. You'd be surprised; with the right framing, bad facts can become good facts, or at least neutral facts.
Always be completely open with your lawyer.