用with表示伴随的状态，as 后面需要接一个完整的句子，即as后面的句子需要有主语和谓语，很明显set在这里是被动的，不能作为谓语，所以用with. 其实这句话是省略了having been, 即这句话也可以是 With his goal having been set, 表示被动。。如果要用as的话，必须是是这样：As he has set his goal, he is really busy these days.