I am not sure what you mean when you ask how Parliament could do this "sincerely." I am going to assume you are asking how they could just go and declare that there was a separate English church with Henry VIII at its head. I assume you are thinking that they should have realized that they could not just make a new church by law -- that only God should be able to decide who heads the church.
If this is what you are asking, I would argue that what Parliament did was no worse than the way that the Pope was already acting. In other words, it's not like you had the Pope acting in a religious manner while Parliament acted badly. Instead, think about why the Pope wouldn't let Henry have his divorce. It was a political reason, not a religious one that led to this. The Pope was pretty much a prisoner of Catherine of Aragon's nephew and so the Pope had to do what he said.
If the Pope is making his decisions based on something other than God's word, then why should Parliament feel bad about breaking away from the Catholic Church?