why not runat = "client"

Somewhat strange and cryptic notation, I agree. It would be clear if runat="client" worked, but, to best of my knowledge, it does not in ASP.NET, or it would be a bogus. I cannot explain such assymmetric notation and I doubt the explanation would be rational.

The idea of running at client is completely different. Everything written in ASP.NET page is generated in response to HTTP request and sent to client in HTTP response of the server. It can contain any MIME type, any content at all, and, first of all, HTML page with any scripts which are executed on client site as usual. That's basically it. Everything else is just the tools for convenience of writing this contents and scripts; for example, you can register client-side script on ASP.NET page and the like, but you can simply write some script code, use other scripts and libraries like jQuery, and so on, so forth.

—SA