What you have to do is play his game of a straight line.
A straight line is just that straight. A straight line from anywhere on the globe would go on indefinitely into space, not follow the curvature of the earth. Lay a straight edge on a ball and where does it go? I doesn't follow the curve of the ball it forms a tangent to the ball. The definition of a straight line you mean is following the curvature of the earth. If you are exactly at true north you can only go south on a globe, no other direction. You need to restate your question by saying you will follow the curvature of the earth in a never deviating path or something like that.
You also have to remember that the RE has an axis, so leaving from true north is problematic. For example: if you are even only say 2 feet off of true north and head east you will go in a little tiny circle east in a 4 foot diameter around the axis. It would also help to start on the equator and then travel east because then you are at the widest point on the RE model and east west travel works very well. But east west also works very well in FE except distances get very long in the south.
Does this help with the argument?