Does letting my bike roll on a hill damage the transmission?

I read on the Owner Manual saying "Towing your vehicle can cause serious damage to the transmission"

I am curious about the reason.

There is a hill before getting home. It's a block distance. So everytime when I get home, I turn off my engine and let the bike roll itself to home. It brings me comfortably home and save some petrol.

Will it damage my transmission?

 

my variator nut came loose once, and with no tools with me, i had to push it 3.5 miles home wearing full winter riding gear.

i arrived home a couple of hours later, shattered and wet through with sweat, the transmission fine.

The gearbox at the back is splash fed with oil, so would be none the wiser whether your engine is on or off, the cvt is a belt on 2 pulleys,
again i cant think of any damge that could occur. The fuel you would save would be negligible i would of thought.

 

i think the same
so why they say towing will damage the engine? Of what mechanism?

 

Would help to know what vehicle we’re talking about...

On many bikes the oil pump is driven by the running engine

 

mine is Toyota SH125I