What are straight lines? On the plane, the straight lines are the locus of the point where the direction of motion does not change.
On the sphere, we can regard any given circle as the circle of latitude (the equator is a special circle of latitude). The point along the circle of latitude movement, is the east-west direction of movement, that is, the movement does not change direction. So circles on the sphere are straight lines . Great circles are straight lines, and small are straight lines.
So circles are all straight lines on the sphere, so,Through a given point, only one line can be drawn parallel to a given line.
On the sphere, what is the tangent of the circle of latitude? The tangent of the circle of latitude is the circle of latitude itself. So the slope of circle of latitude equals zero. On the plane, the slope of the straight line parallel to the X axis of the coordinate is equal to zero.