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In the PDF, the author says something to the effect of parallel lines on the sphere always cross, and points to the longitude lines in the graphic as an example. But the same example shows lattitude lines that appear parallel on that surface, and don't cross.

Does anyone know why there is an apparent contradiction?

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It's because "latitude lines" aren't really lines in this context (except the one at the equator).

If you took two points from one of those latitude "lines", you'd always be able to find a shorter path between them than the path along the latitude. If you take the shortest path between the two points and extend it all the way around the sphere, you'll end up with a great circle. That great circle is an actual "line" in this geometry.

https://en.wikipedia.org/wiki/Spherical_geometry

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