Remember that the goal of any company including EA is not to make games, but to make money. They calculate they'll make more money by forcing people off the old games (at least the online parts) with the hope that some or most of those people will then upgrade to the newest version of the franchise:
All of us at EA would like to thank you for your valued participation in our online gaming community and hope that your enthusiasm for these games extends to our current lineup and beyond.
Other posters have expressed the hope that they'll release source code to the old games so that community-run versions of the servers can be developed. I submit that EA has a greater monetary incentive to keep the source closed - they can save a ton of money on development costs by slapping a new logo on last year's game, changing the version string, updating the player names, and releasing it again next year.
(soapbox alert) So why even play these games at all? What do you get after an hour of playing video games, besides a headache and high blood pressure? Why not go play an instrument, or play sports for real, or do something to improve yourself or the rest of the human race?
You can't take damsel here now.