It _is_ taught to 16 year olds in Australia, if they elect to take math C (math a/B is compulsory where math A is remedial). Everyone hated it and wondered what the point was (including me - it was only when I did a course on abstract algebra in university and learned about quotient groups that I was converted)

Also covered in math C is the computational parts of linear algebra (e.g. Gaussian elimination, Cramer's rule).