I don't know the origins of the phrase, but I do know why I use it and why it makes sense to me.
To me it is a shortened way of saying something has begun the shedding process.
"My ball python has gone into shed"
"My ball python has started the shedding process"
The first one is easier to type and say. It also doesn't sound formal like the second one and every still understands that they mean the same thing.
That's why I use the phrase because it makes sense to me and is a more relaxed way of speaking.