Lyric discussion by therunaround90 

Cover art for Miss Sobriety lyrics by Cute Is What We Aim For

it seems more likely to me that the song is about a girlfriend who was actually the one with the drinking problem. And calling her "Miss Sobriety" may be sarcasm. He asks if she remembers how to say his name. He also says,

"one man's trash is another man's treasure (don't you wonder why i even loved her)"

which might be talking about how to others she was looked at as trash. and people wondered why he was with her. then the "i never thought that i could get so low" might be him realizing that he's settling for a girl who drinks too much and isn't worth his time. he thinks he can do alot better than her.

or it may be about a girl he took advantage of who was drunk, and feeling regret about what he did. that may be another possibility.