I am sure the advocate performed just fine. The law for unemployment benefits is straightforward and the facts you stated do not seem convoluted. Generally, you are entitled to received unemployment benefits UNLESS you voluntarily quit, or committed an act of misconduct. If you voluntarily quite, you would be disqualified to received benefits unless it is found to be for good cause. From what you stated above, you voluntarily quit. Hence, you would not be entitled to received unemployment benefits. You still had to answer truthfully at the hearing of why you are unemployed. And the reason is that you voluntarily quit.
Your last step, if you truly feel that you are entitled to unemployment benefits, would be to appeal the decision by the administrative judge. The ruling that you received should state the reason that the judge made, and the process and time limit you have for appealing it. In this appeal, no new evidence will be submitted. The appeal board will just look at if the law that the judge used to make his or her decision was proper.
From what you stated, it was. You voluntarily quit, and were denied unemployment benefits because of it.
The above response is general information ONLY and is not legal advice, and does not create an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I do not represent you and you should seek the advise of an attorney before taking any action related to your inquiry.