UV unwrapping: Blender always selects an edge ring as a "seam" So I have the following issue:

I'm trying to unwrap the top of this platform. 
I choose some vertical seams on the sides (screenshot), with the objective that the unwrapped model will look like it was flattened from above.



The problem is, Blender always seems to choose one entire edge ring as a seam. I tried "Clear Seam" and "Clear Edge", with no results. This is causing some vertices split, and is giving me some problems when painting the texture.

Is there a way to tell Blender NOT to cut through a specific edge when unwrapping? 



Hopefully you guys can help me achieve my expected result :)

Thanks in advance!
This is often happening when the mesh of your model is not all connected.

To merge vertices placed in the same position:


Go into Edit Mode Tab
Select all A
Open Specials menu W, select Remove Doubles

Unwrap the model again