I play EVE because the PVP is top notch...it's still the only video game that can leave me winded and shaky after a fight...but that's all just a bonus.
It's mainly because of the scope of the playing field.
Everyone I know plays MMOs, and they all talk about funny or awesome moments within them, the asshats they meet, and the conflicts present. I let them all finish. Then I give them the latest from EVE.
Most of them at any gathering don't believe me. They 'pshhaw' and think I'm showing them up, until some of the more learned of the group invariably say "Yeah, I hear shit like that about EVE all the time. It's more hardcore than any of you."
I watch my roommates and best friends play their WoW and AION and Lineage and Age of Conan. We all run guilds and websites and ventrillos, we're all RPers, but I see the day to day stuff in their play, and I can't help but feel like an F1 driver watching a go-cart race. Running a corp in EVE is nothing like it, and doing RP in EVE is a whole other beast.
Mainly, it's a maturity level. Stupid roleplayers in other games get bogged down in whiney he said-she said bullshit that is just plain retarded. Sure, it happens in EVE too, but when a friend asks off-hand for some advice with a problem member, my responses of "Take their shit, kick them from your guilds, start a campaign with your fighters, hire some mercs for timezone coverage, and drive them from the face of your realm" fall on shocked ears. "Oh, sure, that's how you'd do it in EVE..."
And sure, I'm talking all big and tough here, but it works on the other end too. Who am I in EVE? If someone with real power wanted me destroyed? I would be hunted, watching my every move. When I'm out and about on my lonesome on various projects around New Eden, I know I have enemies, and I am not some invincible juggernaut. Anyone with a brain, some patience, or just a fleet and some luck can put me out of commission. That lone frigate pilot with a set of balls can happen upon me and wreck my entire day. I can never let my guard down. A healthy level of paranoia makes for an extra-long clone-life....and it's nothing like any other game that coddles you with safety, that removes that rush of 'making it another day'.
Because EVE is the only place you can do anything besides inconvenience someone with a long respawn.
EvE is not just P-v-P.
Player vs Player is an idea with attached ideas of consent and 'harassment'.
Everyone vs Everyone is a whole other dish, and if you can't handle it, you're booted out on your ass.
E-v-E is EVE.
And no matter how many times I get sick of it, I always end up back, because nothing else comes close. Looking at the long-term projects of the gaming industry, nothing will come close for many years. MMOs are frightened creatures from birth, wrapping their players in bubble-wrap, and shoving them into instanced, pre-written content with no consequence to anyone. When that content runs out, and the grind peaks in a certain set of gear or 'levels', then the game is completed.
You cannot complete EVE.
I play EVE because gaming as a whole is too pussified to do any better.