When you have caught him red-handed and that too twice, naturally he will be feeling defeated- frustrated from within. This might be resulting into the anger. Accepting your weaknesses in front of him will only give him chance to exploit you and that is what exactly he is doing. When he knows that you cannot leave him, he is threatening you that he wants to leave you!
Alcoholism may be root cause, effect or merely an associated problem. It needs to be tackled medically.