Reading all the responses to this problem I have finally figured out where I was going wrong. It always looked to me like the final decision was a 50/50. I just realized I was assuming that the information given by the host was neutral. (Not in a technical sense my math lingo is back to nonexistent by now.) The constraint on the host to open one of the doors which the contestant did not pick gives the advantage to switching. If the host could open any door the advantage would be lost.

For example, doors A & C have goats, door B has a car. I pick door C. The host has to pick one door that has a goat. He picks door C. Now my chance of getting the prize is obviously 50/50. I must choose another door. When the host is constrained to pick a door that I haven't chosen he is giving me extra, though not definitive, information.

The original way, I pick a door. My chance of being wrong is 2/3. The host removes a goat that I did not choose. Because the host could not choose my door, it still has a 2/3 chance of being wrong. I should change doors. If the host could have chosen my door it would have lost that advantage and my chances go to 1/2.

I hope this is clear enough to help anyone who still has trouble seeing what is happening.
Beth