Emotionally speaking, P!nk's work reminds me a lot of John Lennon, particularly his solo stuff.
Family Portrait and Mother both deal with childhood dysfunction - and both end with the singer repeatedly pleading with one or more parents stay.
Sober and Cold Turkey both deal with drug addiction.
Please Don't Leave Me and Jealous Guy are apology songs.
I'm still trying to think of a John Lennon song comparable to Don't Let Me Get Me.