The expression “no ifs, ans, nor buts” means no back talk; no impudence; no argument.
Our British cousins, from all that we can gather, limit this expression merely to “ifs and ans,” as in the meaningless doggerel that my brother and we used to recite,
If ifs and ans
Were pots and pans,
There’d be no use for tinkers.
a slight variant, we believe, of an overseas doggerel. The older expression just means “if”; hence, a supposition.
But our American expression is a negation and of much stronger force.
A parent who uses it does so to end all argument: there’ll be no if (no supposition), no an (an archaic form of and, hence, no condition), and no but (no exception).