You are right, in that the major scale uses notes from its relative minor scale - PROVIDED we're talking about the Aeolian mode or natural minor.
Be aware that a relative minor set of notes will vary with the other two minor scales. In the MELODIC minor, (classical), the 6th and 7th notes are raised by a semitone, usually on the way up, and it reverts to the natural minor notes descending. The HARMONIC minor only raises the 7th (leading) note. Thus, if you follow the WWHWWWH circular pattern in your question, it won't fit for any except the natural minor(relative)/Aeolian mode.
You asked the reason - it's because in the major, the notes gravitate towards the root, say, of C, whereas using the same notes, with a 'minor' feel, they gravitate towards A. This actually works better from our human point of view when there is a G# rather than the G natural found in the parent relative major.