I think the main reasons have already been mentioned, for me it was really all about the novels. We did start some Dragon lance campaigns including the first module of the official Dragonlance Chronicles adventure but I think we got stuck between do you act out the offical story/do your own thing conundrum that I've heard people talk about with licensed RPGs.
We all loved the books though and as far as I go the main things that stick with me 30 years later are
(Where it all began for me and my friends. I reread them both not that many years ago and I felt they both held up well. Better than the Icewind Dale trilogy by a long shot. At the time I preferred Chronicles - I guess the classic hero's quest and clear evil to be defeated made it easier to like than legends many greys and shadows and not entirely being sure who you should be cheering on but rereading them I think legends depth took the lead. Its like when you watched Return of the Jedi as a kid and you loved the Ewok bits on Endor but Luke and Vader on the Death Star was too talky talky but rewatching them when older you realise that throne room was where all the intresting character bits are and the Ewoks are just stupid, except Chronicles is still good and not the galactic empire's finest troops being defeated by a teddy bear throwing a stone at them.
- People on the good side who were jerks (looking at you leaders of the knights of Solamnia) or at least flawed (keep it in your pants Tannis).
- Bad guys you liked but were still actually bad. (Kitiara, Lord Soth)
- Bad guys you liked but weren't sure if they were really bad guys. Or if they were, how bad they were (Raistlin, Dalamar).
- Huma and Kaz the Minataur
- The art. Oh yes the art!
- Lord Soth
- Flying citadels.
- Pictures of Flying Citadels.
- DRAGON LANCES! I mean people riding dragons with magic lances engaging in dog fights with other dragons. Seriously how cool is that!
- Kenders, gully dwarves and gnomes (yes all of them - especially the gnomes)
- Characters turning out to be a, gods b, dragons c, dragon gods d unexploded sentient spells.
- Heroic angsty deaths, tragic deaths, tragic backstories. Emotional catnip. (you'll buy 20-30 more books in the series long after the quality has dropped to keep getting those hits)
- Lord Soth
- The Cursed grove of the high tower of sorcery in Palanthas.
- More art.
- Epics wars and personal stories wrapped up in each other.
- God's that are actually interesting.
- Weasle's luck and Galen Beknighted - two stories about a shifty son of a podunk knight of Solamnia in a swamp based castle facing a small local evil. A million miles away from world level battles of gods yet still Dragonlance.
- Actually both the Heroes and Heroes II trilogies. Storm bringer and Gates of Thorbardin were good too. After these books only really the preludes held up the quality by Preludes II it was going downhill fast.
- Lord Soth
One last thing my friend used to joke that Weekender by Flowered Up was actually called Wee Kender! and we ended up with a running joke that if Kender came up in a conversation we would start singing it.
Just to note Weekender is a) one of the greatest musical achievements of mankind and b) a 13 minute long structureless track that got the band dropped from their lable that embodies the Baggy/Madchester scene (although they were from London) and appeals to only approximately 0.000003% of the worlds population so your mileage may vary.
But my nostalgia runneth over so it's too late to stop now.
So one last time. All together now.
"Wee Kender! Wee Kender!
Go out - Have a good good, good good time"
Edit - just remembered there is a moment of swearing about half way through so NSFW.