Wearing hats in church

Having been brought up in the Anglican tradition, my parents always made it very clear that there was a protocol about who was allowed to wear a hat in church.  Gradually I became aware that for earlier generations it was not so much a case of being allowed, as who was expected to wear them.

Basically ladies wear hats to church and gentlemen take their hats off to go into a church - or even a house.

There are some notable exceptions.

Archbishops take their hats off outdoors but wear them in church.

Bishops and archbishops do wear something on their heads in church, but it appears that they take them off outside and they are not allowed to be ladies.  Their headgear looks like a hat, but it is really a mitre - so perhaps it doesn't count.

Now that I am no longer a Christian I think I know the bible much better than I did when I was one.  In that capacity, I suspect that this is the passage that is used as the basis for the rule.  As usual, it is not completely and unabiguously clear what it really means.

A man ought not to cover his head, since he is the image and glory of God; but woman is the glory of man. For man did not come from woman, but woman from man; neither was man created for woman, but woman for man.  1 Corinthians 11:7-9

Taking that as the rule (which I find to be disrespectful to my equal female friends) I wonder why it only applies in a church.

Should I think laterally like this?  It might be seen as a total lack of focus (as some of my colleagues appear to think).

I prefer to think of it as a strength.