A "but-head" is a phrase at the beginning of a sentence meant to "preemptively deny a charge that has yet to be made" and is usually followed by the word "but."  For example: 
  • I hate to be the one to tell you this, but...
  • With all due respect
  • I hear what you're saying, but...
  • I'm not trying to hurt your feelings, but...
  • It's not about the money, but...
It's similar to a non-apology apology like "I'm sorry if you feel insulted" and a non-denial denial like "I'm not here to talk about the past."  We talking primates have many different methods of lying.  (via Kottke) #language