on his arrival at school ,he visited his former teacher.为什么用his arriving是错误的

arrive 本身就有arrival 作名词,因此arriving 是不选的.
但如果一个词没有相应的名词形式,却非要用那个词时,才用这个动词的ing形式.
如：
Do you mind my smoking here?(作为一个动作,smoke没有相应的名词.smoke作名词是烟雾的意思)