I think you are correct but you do not go far enough.
Why does the world hate Christianity?
Because our very existence as Christians convicts them of their chosen sins. The Holy Spirit within us cannot be silenced and our very presence in their lives forces them to confront their own evil. A confrontation that they desperately want to avoid.
They do not hate the Catholic church because it is Catholic (although with the present pope it is becoming less Catholic and less Christian each day). They hate the Catholic church because it is a church made up of mostly Christians.
If the organized church (all Christian denominations) ceased to exist, this reaction from the world would be exactly the same. The world hates Christians because Christians serve as a testimony to their own fallen state.
This also explains why no other religion (even the satanic death cult known as islam) is hated as Christianity is. A moslem does not force the world to confront their own evil. Moslems are just as lost and evil as they are and so they pose no threat. Moslems do not have the Holy Spirit in them convicting the sinners of their sins. Any made up religion will be accepted.
Christianity is hated because Christianity is true.
Another reason FR needs a like button.
This was the same reason Jesus was hated by the Pharisees. His presence highlighted their hypocrisy. Darkness hates the light.