Ok, so then you also know that web servers don't maintain a persistent connection. Which means that the connection doesn't stay alive. Which means as soon as the web server is done dishing out the web page to the client (or any information to the client) it immediately disconnects. So... let's follow this scenario:
1) you connect to the web server
2) buddy connects to web server
3) web server d/c you
4) buddy tries to send you a message, and is also d/c
5) web server..... does what? Sends you a message over a broken TCP connection?
Omg... You and your buddy are connected at the same time. When the server receives a message from one, it forwards the message to the other person. So their both connected to the server, and the server responds to their connection.