I can understand from the image that the transmission wires are swapping with the receive wires, and I know why that is important, but I'm struggling to see why the right hand side shouldn't be vertically flipped from what it is in the image above.
My thoughts are this: imagine a laptop with an ethernet port on its right side, and on the left hand side of the port is the TX+ pin. Now imagine another laptop on the right of the first, with an ethernet port on its left side and, again, having the TX+ pin on the left side of the port. The crossover in the image above would connect the RX+ to the right side of the rightmost laptop's port, so that rather than connecting to the TX+ it is connecting it to one of the unused wires.
I'm not sure how confusing that came across, but I've (badly) drawn a diagram to try and show what I'm trying to explain (L meaning left relative to the arrow, and R meaning right relative to the arrow, with the arrow just being the way the port is facing):
Which part am I getting wrong?