1. 你老师说得对,此句的them的确多余,必须去掉.
2. 解释：
1）原因很简单,因为to put on中put on的宾语就是句子的主语my shoes.
如果再用them的话,就和句子主语my shoes就重复了.
除非这里有两个句子,才可以再用them来代指my shoes.
3）例如：
My shoes are too small to put on.
= My shoes are so samll that I can't put them on.
第二句就含有一个that引导的结果状语从句,此时就必须加上them,因为此句中put on的宾语不能缺少.