Having been married somewhat at different stages in my progress towards the grave I'm very much in accord with the title of the song and sing it from the bottom of my heart. I've learned it from Soodlum's 100 Irish Ballads Volume 1
which describes it as dealing with a woman who while broken-hearted when abandoned by her lover drowns herself. Sometimes I parodize the song by gender changing i.e. instead of singing "I'll be no man's wife", I sing "I'll be no woman's man".