""""""""""From 6:30 to 7:10 on the video I am baffled since Carvewright mirrors the profile for a reason unknown to me and uses it for some purpose."""""""""

At that point he is trying to "sweep" the profile he made around the 2 circular arcs. With the sweep command, it has an auto placement and orientation that it does. Notice he sweeps the profile, then gets a result that he wants flipped the other way. So he "mirrors" the profile, basically reversing it, then does the sweep again and gets the result he wanted (the direction and orientation of the sweep result flipped)...