Why can't we use C programming language for designing webpages?

Answer 1

No, you cannot. While it's possible that a web server may be written in C, an actual web page relies on HTML and various specialized languages (JavaScript, PHP, ASP, etc.) Note: You might write CGI-programs in C, if that's what you meant.

Answer 2

For the simple reason that noone could be bothered mainly.

In a sense, we already use C to build webpages. All of the core of PHP is written in C. And you could theoretically create a C program whose output was HTML. That would allow you to create the HTML in C. Plug it into a server architecture and Viola! C based webpage.