I'd never heard this expression before, but I think it's a little bit beautiful. I might try it out some time.

I suspect self-confess means that one confesses to oneself.

For example, if I were previously in denial about being a gambling addict, and one night I realize, "Lo! what they've been telling me is true. I AM a gambling addict." Then I will have self-confessed.

The chorus of the song goes:

"Don't wanna hear you say
Ain't nothin' but a heartache
Ain't nothin' but a mistake
(Don't wanna hear you say)
I never wanna hear you say
I want it that way"

They explicitly say that it's a mistake. The Backstreet Boys don't want this person to say "I want it that way" because it's a grammatical error.

or maybe it's a typo, and the expression is "I love you hat"