It's not simply EA not wanting their game sold through Steam. EA sells through other online game distributors. The problem, from what I've heard, is that Steam's terms changed a year or so back to require DLC content to be distributed through Steam -- they wanted a piece of that pie. If a developer tried distributing DLC for a game through means outside of Steam, Steam would not allow it on -- this is why Dragon Age II and Crysis II were originally posted on Steam but were taken down. But now, Crysis 2 is actually back on Steam -- the Maximum Edition, which includes all of Crysis 2's DLC directly and EA has no plans for new Crysis 2 DLC.
So it's not as simple as "The evil hellspawn EA despises the white knight Valve and seeks to destroy it by withholding their games". Valve has terms that EA has to meet if it wants to put its games on Steam. EA doesn't want to comply to those terms and doesn't see having its games on Steam as important enough to make them comply -- they think they can make it on their own with Origin or other, less popular online distributors. Now, you can go ahead and hate on EA all you want for not caring enough to make its games acceptable for Steam, but the ultimate decision to keep EA's games off of Steam isn't EA's, it's Valve's.