Question

Why is the stateless nature of the internet a problem for shopping cart software? g?

Answer 1

In a stateless connection, each transmission is independent, no continuous connection is maintained.  Stateless system is a problem for shopping cart software because it does not keep information from one transmission or session to another, thus shopping cart must store information about specific shoppers and their purchases. 

Answer 2

Web applications should be understood to be stateless unless there is a good reason to be stateful. By design, a shopping cart is a stateful feature and not accepting it as stateful could be quite counter-productive. The whole point here of a shopping cart is to preserve the state nature of the application between requests.
In other words, the stateless nature of a shopping cart means it does need to care about who I am or what orders I have placed and this might end up being a problem. It will not be able to maintain a shopping cart full of goods.