There is a hole in your boy's psychy

left there wide open by his mother's physical and emotional distance.  The mother may have her own uneasiness to cuddle her boy, and the arrival of the sister offered her a good excuse.

The time to fill the hole by the mother may have passed. The effect of this empty space and his unwitting effort to fill it himself are already manifesting.

His quick temper is a result of his perception of others' inadequacy, triggered by the anxiety and frustration conditioned by his mother's absence or distance when he needed her.

His effort to explain the math question to the girl is because, in his mind, such inadequacy needs to be addressed and no one else will do it, even though he had wished otherwise.

You son will not spend the rest of his life trying to fill that empty space since, fortunately, you have recognized the problems and started to fix them.  Knowing the cause of a problem is halfway toward solving the problem.

One thing to try is to remined your son to value himself, to be responsible for his thoughts and feeling, be a master of himself because he is worthy of such responsibility.  Do not distract himself by focusing on somebody not doing something, focus on what she is good at doing.  Be aware of his own breathing, modulate the air flow to and from his lungs.  Take charge of setting the tone of a conversation, and remember there is always a better way of saying something.  If he sees someone with a long face, the first question he is to ask is "Am I smiling?".

Chinese children have a lot burden on their shoulders, placed there by their parents.  When you carry a lot of others' stuff, your own stuff gets dropped.  You'll no longer be your own person.  You will not be whole.  If everyone is like that, it is not too bad.  Otherwise, you are at a distinct disadvantage.