I am new to Github Pages and was just trying out the links to some pages. username.github.io works, but www.username.github.io does not. Why is that so? I understand that the answer will be in some corner of the internet, but I did search it and failed to find an explanation for it.
That is due to the simple fact that Github has not configured their DNS records to support this naming scheme.
While this is entirely possible using wildcards, see Wildcard DNS record, the web has been shifting away from the www convention for some time now.
The reason why this is happening is very subjective, so it is not in the scope of Stackoverflow to answer this, but it can be inferred that given the ubiquitous nature of the World Wide Web, the shorter an URL is, the better it is, if just to allow people to more easily remember them, and type them.