Because the Scots have a long history of hating the British.
Don't you mean the English?
When Scotland and Wales are independent, will the English still be "the British?"
There is no "British language." The Welsh and Scots are as British as the English are. And there is no such thing as an "English Empire."
Furthermore, the Anglic Protestant lowland Scots are traditionally enthusiastic Unionists and were even more opposed to the Jacobite rebellions (which weren't wars for Scottish independence, btw) than the English were.
Sorry. This confusion of Britain and England is a pet peeve of mine. Maybe when Scotland is independent it will change its name back to the Kingdom of England and we'll have heard the last of "Great Britain" as anything other than an island.