I go to my church on Sunday.
Someone keeps arguing it is correct but it feels like my church implies that the speaker owns or runs the church.
I feel that the more appropriate sentence could be
I go to church on Sunday.
But then argument continues,
My church is in this/that area.
However, I feel the more appropriate sentence could be
The church is in this/that area.
Also, office (where the person works but doesn't own), school(speaker goes to this school but doesn't own, house(speaker lives here but doesn't own) are used in the argument.
Is the use of my in the sentences above correct ?