Anyone who has read UT, and specifically The History Of Galadriel And Celeborn, knows that in all of Tolkien’s writings regarding the history of M.E., there is no part more full of problems than the story of Galadriel and Celeborn.
As Plastic rightly pointed out, Galadriel was of the Noldor (in fact greatest of all the Noldor save for Feanor, but greatest of all Elven woman), and depending on which version you personally choose to cling to, Celeborn was either a Nandorin Elf (one of the Teleri who refused to cross the Misty Mountains on the great journey from Cuivienen), or one of the Sindar.
There is also a wholly different story on Galadriel and Celeborn which was one of J.R.R.'s last writings on the subject, and according to Christopher Tolkien, one of his father's last on M.E., written in the last month of his life before he died. This version has Celeborn and Galadriel meeting in Alqualonde (contradictory to the version in The Silmarillion, where they met in Doriath), and Celeborn is a Telerin prince, grandson of Olwe of Alqualonde, and thus would have been one of Galadriel’s close kinsmen.
So again, it’s just a matter of which version one chooses to cling to, and depending on which one you prefer, Galadriel and Celeborn may, or may not have been related. Since the versions in UT come from unpublished (at the time of J.R.R.’s death), and unfinished writings, I personally choose to refer to the version in The Silmarillion, since it comes from a completed narrative, and also since it eliminates all of the problems (although I do like the last version Tolkien was working on, because that version has Galadriel taking no part whatsoever in Feanor’s revolt).
In the version in the Sil., Celeborn and Galadriel meet in Doriath, and Celeborn is the kinsman of Thingol, and of the Sindar. Getting back to the main topic of this thread, in addition to the reasons that Grondy has already listed, the fact that Celeborn was a kinsman of Thingol’s, and resided in Doriath, would have been major factor's as to why he was so bitter towards the Dwarves, since they were responsible for the sacking of Doriath, and the murder of Thingol.
Hopefully I haven’t just added to the confusion here. I’m still far from an expert on the Elven lineages, and they can be very difficult to keep straight. Maybe Val, or someone else can come in here and do a much better job of explaining this than I have.
"I would have the Ring-bearer bring the crown to me, and let Mithrandir set it upon my head, if he will; for he has been the mover of all that has been accomplished, and this is his victory." Elessar