-- I don't know this person
-- The invitation was spam
There was no "other" option presented. And, notably, the usual reason why I ignore LinkedIn invitations was missing: I just plain don't want this person in my LinkedIn network. I mean, I do know him slightly, from an online forum. I have found him to be a somewhat self-important ass who doesn't listen to other people. My primary criterion for accepting a LinkedIn invite is, "Would I recommend this person for a job?", which requires knowing someone pretty well, and trusting their ability to perform well in their chosen field. He doesn't qualify.
Of course, I simply ignored LinkedIn's request for a reason -- I essentially said "other" by closing the window. But there's a subtle social pressure there, a message from the service (and I'm not sure whether they're doing it intentionally) that the only *legitimate* reasons for ignoring a request are because it is abusive. That's a dumb mistake, especially for LinkedIn above all the other social networks. Their only real advantage is the fact that people *don't* use it like Facebook, accepting friend requests indiscriminately; folks who understand it well use it as a Rolodex, building up more genuine trust networks.
If LinkedIn was smart, they would be focusing on that -- encouraging *better*, well-defined networks, which requires a real measure of selectivity. Instead, they seem to be tacitly falling into the usual social-network trap of assuming that Bigger Is Better. They may come to regret that missed opportunity, especially if somebody else figures it out and pounces...