Why doesn’t neutral wire give a shock?

If you are touching neutral wire same as above current has two options
 a) it can enter your body and reach the ground.
 b) it can go continue travelling through neutral path.
But here the first case involves passing through your body resistance and reaching the ground whereas second case is passing through neutral wire with almost zero resistance (its an express way for current).so the current will logically choose to avoid your body path and will happily flow through neutral.

Normally neutral is earthed at substation, so chances of shock is very less.
In addition of this, if due any reason, earthing become week, neutral can give shock also.