Why Is It?

[Flyhalf]

Why is it that I can draw a straighter line (freehand) left to right than up/down?

[wildwood]

Maybe because we write left to right. Try doing it with the other hand, you may be surprised.

[Flyhalf]

Thanks, Wildwood. While your reply doesn't explain why this happens, your method does seem to work.
I'll have a go at using right hand for L-R and left for up/down (not much improvement on the L-R axis with the left hand).

[jomifl]

When you draw a line left to right you may be resting your arm near the elbow and are swivelling it whilst correcting the radius effect with your wrist. To draw a vertical line the arm has to be free from the shoulder down so requires finer control by the shoulder muscles. I've just tried it with my arm free from the shoulder and I can see little difference between horizontal and vertical.

[modeller]

Fewer muscles are needed. Your eyes and you head move more easily in the horozontal.

[DaisyNonna]

Because you have been trained from childhood to track from left to right whilst holding a writing implement. Or, simply you write from left to right.