I think he's got you defending a straw man.
1) Judeo/Christian morality is always changing. He implies that it doesn't, and that, for some reason, becomes an axiom in this thread.
2) He implies that there is some kind of virtue in unchanging morals, and that gets your back up. Yet, Christianity is a revolution of new morals, slowly replacing Judashit. There is no evidence that unchanging morals are somehow better, yet that has also sneeked in, as an axiom.
Christianity proves that man can keep developing morals, even when people think they are fixed by a sacrifical religion that would kill people who worked on the sabbath. Paul made some of the first steps away from Judashit, but he denegrated women and homosexuals; encouraged servititude to the state, and didn't say anything about slaves. Matthew wants to keep people adhering to the whole law, inc stoning raped women.
I'm sure that morality will keep getting more advanced, even if most Christians want to hold us back, and stop us following Christ's example.