The Internets are full of explanations of the President's odd choice, some more convincing than other.
1 - Quid pro Quo Miers knows a secret. She was appointed to the court to prevent her from telling the world that W's still drinking, or that Karen Hughes actually does change the president's diapers. Or somethng like that.
2 - Fear The president's men are worried about some of the cases (Plame, torture, etc) now winding there way up to the Court. Miers was nominated because the President trusts her to carry his water.
3 - Arrogance The media says I appoint too many cronies, so goddamit I'm appointing cronies! Ha! Take that!
4 - Stupidity It's possible, some posit, that the president just doesn't realize his personal lawyer, a woman who has never been a judge, might not be qualified to sit on the highest court in the land.
5 - Cynicism Many have noted that it would be bad for business (the business of GOP politics that is) if Roe vs. Wade were to be overturned. All those hillbilly state senators and Assemblypeople would have to actually do something about abortion instead of just fulminating about it impotently as they do now. The polls say that in many places a state law against abortion would put many of those loudmouths out of a job.
6 - Ignorance Perhaps the president really does believe that his old friend is the most qualified person for the job. That's not impossible -- expecially when you recall that this president brags about ignoring newspapers, thinks that Jesus was the bestest philosphicalwhoozit of all time, and needed the cliff notes to get through My Favorite Goat.
What did I miss?