Leaving edge Upon Face Deletion

I'm going through a series of surface design videos. What I'm trying to do is delete a surface body, and leave two lines on the surface that intersects the bodies.

Here is the example of what I'm explaining. https://www.youtube.com/watch?v=b1ny_3M-j6U&list=PLUgk_zEXfs_UQE35wUr0QEuCbJbefs0NX#t=374

My file has the result I'm always left with. I've tried different selection order, re-extruded the surfaces ect. Including clicking show tangent edges.

The result.png is what I'm trying to achieve which is the blue lines and what I end up with is my_attempt.png

Not sure how to leave the edge, hope you can help.

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He is deleting the 0.4mm gap between the extruded surface and it's offset- you were deleting a part of the extrude. In the attached snip from his tutorial you can see the gap where the surface has been trimmed in this gap (06:22 in the youtube video).

 
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