Why would I want to turn off the Ring of Basilius?
Solution 1:
There are three main reasons.
When you are giving an armor bonus to your creeps, you will end up pushing your lane towards the enemy, which is something you do not want to do as you're granting them improved safety and risking a gank to yourself.
Sometimes, you may want to toggle it on and off randomly when in lane to mess with the enemy hero timing in their attempts to last hit your creeps.
As AdamP pointed out in the comments, the aura may give you away if you are invisible or hiding nearby.