I have seen the calculation for the separation distance of indistinguishable particles versus distinguishable ones. According to Griffiths (Pg. 204 3rd Ed.), the difference in separation distance is $$\langle (\Delta x)^2\rangle_{\pm} = \langle (\Delta x)^2\rangle_{d} \mp 2 \vert \langle x\rangle_{ab} \vert ^2.$$ where a and b represent two particles a and b and d represents distinguishable.
My question is why, conceptually, are identical bosons "pulled together" and identical fermions are "pushed away"? Is there a reason to anticipate this a priori?
