You've been skewered.

Skew lines are neither parallel nor intersecting, occuring in three-dimensional space, not two. Imagine skew lines as an overpass and a roadway passing beneath. They don't intersect, but they're not parallel, and they aren't traveling in the same direction.

Or think of the front-right edge of a shoebox and the top-left edge. They each join two planes, but there isn't a common plane containing both of them.