Please explain why does it hurt my tooth to open my mouth?

Depends: If you mean it is cold or air sensitive when you open, it could be several things. Only your dentist can properly evaluate what is going on. You may have a cavity, sensitive gum line from recession, a crack or fractured tooth. If the pain is just from the movement from your mouth opening, it could be an inflamed gum issue. See your dentist.

Dental evaluation : I can't tell you why your tooth hurts when you open your mouth without seeing you in person and doing an exam including some diagnostic exams. See a dentist to find out what is going on with your tooth.

Can't explain: without having a one on one clinical exam and x-rays. See your own dentist to find out why and what to do about it.