I know you can't and I will never be one to convince you. There are errors in your own church's doctrines and it is not infallible either. We will have to trust God to sort it out for us but it won't come through just one church. Mary
You are very kind and civil, and I thank you for that.
We believe that we do not have doctrinal error, since the Church speaks with the authority given Her by Christ. Nobody else on Earth has that authority, thus the Church, for example, had the right to change the day of Worship from the last day of the week Saturday (Jewish) to the first day of the week Sunday (day of the risen Christ).
I don't think anyone beleives that their church is infailable. I think some folks beleive their church to be guided by the Holy Spirit, as Christ promised it would be, and some folks feel they personally are guided by the Holy Spirit and thus personally infailable with the church being suspect. I think the latter is simply naive frankly.