Answer :

I go to school with him every day. Option B

This is further explained below.

What is him?

Generally,  used to refer to a masculine person or animal that has been mentioned before or can be readily recognized when functioning as the object of a verb or a preposition.

himself; used to refer to a male person or animal that was previously named as the subject of the phrase when it is being used as the object of a verb or a preposition.

his; having anything to do with or being related with a masculine person or animal that has been mentioned before or can be readily recognized.

he;used to refer to a male individual, whether it be a human male, a child, or an animal that can be readily recognized as male.

In conclusion, the correct sentence is

I go to school with him every day. Option B

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