Doesn't it explain the reasons if some book or website says so?
There are a couple of common features that Altaic, Korean, and Japanese languages share, such as:
-SOV
-agglutinative
-vowel harmony
-a word rarely starts with R sound, if not never
-a word rarely starts with double consonant, if not never
As far as I know, however, many researchers think Japanese is not completely included in Altai family. More researchers think that Japanese is some combination of Altai, Austro-Asian, and some other languages.