The start point of the river is only small water spring.
Then, all of natural activity change water spring to big river which head to ocean.
If the water remained at one place...that is stagnant water.
It is easy to spoil, smelling and pollute.
流派 means "branched flow".
The founder of the 流派 just started his BUGEI for himself.
Then, the discipline of disciples and hard era changed 流派 to large.
BUGEISHA shouldn't stay at 流派.
BUGEISHA shouldn't lean on 流派.
If BUGEISHA do so, it is 留派(ryuha:stagnant group).
I believe that the meaning of 流派 is flow itself.