English tends to build new compound nouns by simply writing them as separate words with a blank. Once the compound is established (and the original parts somewhat "forgotten"), it's often written as one word or hyphenated. (Examples: shoelaces, aircraft...) Other languages, German for example, are notorious for very long compunds like this and this, that are made up and written as one word directly. Perhaps the way your native language deals with compounds explains your (or other authors') personal preference and sense of "right"?
Web site / website seems to be somewhat in a transitional stage, being seen as an "entity" that web page hasn't reached yet. Depending on which dictionary you check you will find web site and website, but only web page, not
Edit regarding the use of capital letter 'W' for "Web site":
According to common English rules, you should use a capital letter only at the beginning of the sentence and for proper nouns. Website is not a proper noun (as opposed to the Internet), hence not capitalized. According to your source the spelling "Web site" (and the less questionable "web site") is an anachronism from the 1990s that is still in use by the NYT and some other conservative print media in the US while most others (including the online sections of the NYT!) today use "website". "Web site" / "web site" is only alive in AmE and even there it's used in the minority of cases. So unless you are writing for the NYT (and even then, they have editors), be contemporary, international and play it safe by using "website".