You are probably on the TSA watch list therefore something is popping up on the Alaska system telling them that you need additional screening. It happened to me a lot on several airlines until I went through the TSA vouching process which includes mailing them your birth certificate and other ID. TSA is supposed to notify airlines that your name has been cleared.

It took awhile before Alaska updated their system or maybe they just adjusted their system to automatically allow MVP Golds to do an online check in but it is working for me now.

It was frustrating for awhile because every time I flew on Alaska out of OAK, I would have to wait for a gate agent to go in the back to verify that I am allowed to fly.

I haven't had any problems lately checking in online. Let me know if you have any other questions. You can post to the TSA flyerTalk group as well. I can't answer your question on why Alaska screens you but other airlines don't. Maybe they are just being carefull to follow TSA regulations.