You will never be the reason that your mother drinks, even if she uses your words or actions as an excuse to drink. The reason she drinks is that she is an alcoholic.
There aren't any magic words you can say to her to make her realize and accept the extent of her issues. The best any of us can do is maintain healthy boundaries to protect ourselves from the consequences of another's addiction.
Begging, pleading, yelling, reasoning--none of this will get you anywhere, and will only cause you pain and frustration. I'm glad you found us here. I hope you will stick around.