Question

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

Answer 1

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.

Answer 2

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.