这里his failure 和to arrive early是同位语,就是说它们两者都是主语,表达的都是同一件事情（你迟到即你犯的错误）,所以他们两者任意去掉一个,句子都是完整的.
His failure made him quite disappointed
to arrive early the college made him quite disappointed
如果是arriving early 这就话也是对的,所以这里不是failure in doing sth这个结构的用法,B改成entering 就对了.