Why can't I use HttpServerUtility.HtmlEncode inside a class?

You can use HttpUtility instead, which has a static method that does not depend on HttpContext.

string myString = HttpUtility.HtmlEncode("my link & details");

More info on HttpUtility.HtmlEncode method on the MSDN.

HtmlEncode isn't a static method, and requires an instance of HttpServerUtility to call. Since HttpContext.Current.Server is a HttpServerUtility instance, you can instead use;

string myString = HttpContext.Current.Server.HtmlEncode("my link & details");