"The teacher is a busy job"是否正确?teacher是指人的,那能否说是繁忙的工作?

可以，但在这教师就是作为一个职业了。因为后面说了是job

你是想说teacher这份职业吧。
可以这样说：Be a teacher is busy.

人 是 工作?当然不行
the teacher works busily.
the teacher is doing a busy job.