I need help to understand why difference tool sometimes it works, sometimes not.

Please check the attached file, there are two circles, each one is crossed by a path (line) that passes under each circle from below (each circle on top of each line),
but when you apply path -> difference to each, one works as intended (only the left and right parts of the line remain (out from the circle), but the other deletes everything.

Hi.

The difference tool is running a boolean operation which is based on the area the paths are enclosing.
Two noded paths with straight line segment(s) don't have any area to them.
More than that, by subtracting from an open path, it will create a closed one.
You can see that in your example too: the bottom one creates two "triangles".
Which is, only due to the fact it is not a straight line segment, but a curved one, and having a very small area enclosed. Straighten it, and the difference tool will delete it.

Booleans have about a 0,02 pixel inaccuracy, and, they merge together nodes closer than that.
Which, in this case, pretty much answers why there is no sign at all of the action.