Geography and its Parallel Lines

Something that has always annoyed me whenever I have to do geography work for a class is how teachers try to explain latitude and longitude. Mainly, I have issues when they say that latitude lines are parallel and longitude lines.
In fact, longitude lines are parallel. And not parallel. At the same time. They are parallel at the equator. They continue to go straight, but because they are on a spherical plane (aka Earth), they eventually intersect at a point.
Now that I think about it more, I'm realizing that obviously none of these lines are actually straight. Additionally, what's up with maps? I found a great image on google that highlights the fact that projecting a three-dimensional surface onto a two-dimensional one is very, very difficult. Especially when that three-dimensional object is spherical.

My takeaway from all this is that circles are weird.