1. 你老师说得没错.
句型“It is necessary + that从句”中,要求that从句一般使用虚拟语气,即从句的谓语动词由“should + 动词原形”构成,且should可以省略.
2. 即：It is necessary that he start training before the show.
= It is necessary that he (should) start training before the show.
其中,should为情态动词,其后加动词原形start,所以不能用其三单形式starts.
3. 此语法只需记住即可.