Prepare your brainmouths for my Sennbabble! >:U
The way I see it, "carebear" is to the EVE/gaming community, as "nerd" is to modern society.
If you want to joke with your other computer-gaming, MW2-grinding, D&D-optimizing, anime convention-going, Cowboy Bebop-watching, watched-Titan-AE-ninety-times-cause-its-so-boss friends. You might use "nerd" as a term of endearment. Case in point: "We're planning to get together at Brian's house, watch Atlantis, play some Melee, and just be total nerds for the night."
Nothing insulting there. Now, getting caught by your childhood nemeses in the school cafeteria discussing the finer points of Firefly... well, now you're a nerd, with a negative emphasis.
Same bit with carebear. In certain instances, you might be making fun of your friend for missioning/mining in hisec to make some isk. You might be taking a friendly jab at the one guy in your corp who refuses to PvP, has only hauler losses on his record, but still has fun and contributes to the corp through his intensive indy skills. You see where I'm going with this.
Now, if you're minding your business in lowsec, running an annex, and just that once forgot to check d-scan when a neutral popped up, and several minutes later you're in your pod watching nine Machs, fifteen Vagas and a Curse disappear as you warp to safety, and you happen to mention how you feel about the situation, you know what you're in for in local.
"LOL U MAD CAREBEAR!?!11"
Anywho, point I'm trying to make is, sometimes we're going to mean things in jest, and they'll be taken out of context. It happens a lot. Thats why moderators are here.