Why does supply (and demand) shift left and right as opposed to up and down?
Both ways of thinking are correct. They are two equivalent and complementary ways of thinking about the same thing:


Shift left (right): At each price, the quantity that producers are willing and able to supply has gone down (up).
Shift up (down): To get producers to supply each quantity, the required price has gone up (down).


Example where the supply curve shifts left or (equivalently) up: