I don't hate Palace, I just think the matches are a bit spicy. It should be good fun, but for some it's a boring obsession. As for those who were boasting of the relative positions a few games ago, I hope you are suitably embarrassed.
Boasting about something as transcient as League Position is always an odd one. I am, however, strongly in the "despise Palace" camp. The reason? Their fans. As soon as any Palace fan finds out I am a Brighton fan the abuse it both boring an predictable as well as immature and quite graphic.
Added to that, there were an odd amount of Palace fans at my school and Brighton were awful between 1994 and 1999 (although the tail end of that was brilliant) and I vividly remember Palace fans taunting me throughout the Hereford game (we were on a school trip).
So I have different reasons for my dislike as I was born after the Mullery/Venables feud and I forget about it often. Its very easy to be reminded though when Palace are such a nasty and bitter little club.