While explaining concepts of ASP.NET MVC to my students
MVC is stateless. It is built on top of another stateless protocol - HTTP and HTTPS
MVC is not stateless, HTTP is.
HTTP being stateless doesn't mean it is fire and forget. The client does wait for the response. It is stateless in the sense that two successive requests have no relation whatsoever.
State can be emulated using sessions, for example using cookies.