The church is the Bride of the Christ and Christ is the head of the Church. Should we ever say “my church”? The Christian “church” can be used interchangeably with the “body”, the “woman”, the “wife” and the “Bride of Christ”.
Would it be weird for a married woman to refer generically to “my wife”? Well that would be strange, because she IS the wife.
“And I say also unto thee, That thou art Peter, and upon this rock I will build my church; and the gates of hell shall not prevail against it.” –Matthew 16:18
Clearly, Christ claims the church as belonging to him. Similarly, in apostolic writings, they use a non-possessive part of speech, usually “the” church, as there is but one, but many localities for it.
“And he is the head of the body, the church: who is the beginning, the firstborn from the dead; that in all things he might have the preeminence.” –Colossians 1:18
“For the husband is the head of the wife, even as Christ is the head of the church: and he is the saviour of the body.” –Ephesians 5:23
“That he might present it to himself a glorious church, not having spot, or wrinkle, or any such thing; but that it should be holy and without blemish.” –Ephesians 5:27
“Let us be glad and rejoice, and give honour to him: for the marriage of the Lamb is come, and his wife hath made herself ready.” –Revelation 19:7
As I see it, Christ is the only One who can say “my Church”. It is Christ’s church, and the gates of hell will not prevail against it.