This argument glosses over the countless moral atrocities that were normalized throughout history. From the Crusades to the Trans-Atlantic Slave Trade to the Salem Witch Trials, people have condoned actions that we would consider heinous crimes today, indicating that mankind has not always held a consistent moral code.
Further, this argument asserts that though some minor, less significant moral norms have changed, humanity has "gotten the gist" of morality throughout history, arriving at the most important moral truths early on. This assertion is patently untrue. Although the human race has kept roughly the same stance on moral issues like murder, theft, and cheating, it has changed dramatically on topics that we would no doubt consider crucial today, especially issues of human rights for marginalized communities.