Why do we say that web services are stateless?
Because web services are based on HTTP, which is a stateless protocol.
Quoting wikipedia :
A stateless server is a server that treats each request as an independent transaction that is unrelated to any previous request.
i.e. each request is independant from the previous one : even if we use some "tricks", like cookies for instance, to preserve some state between requests, this is not something defined by the protocol.