What it says is that no individual can be moral if the cherry pick or invent their own values. Anyone who judges themselves by their own values will always pass their own judgment and consider themselves "moral". That thinking has given us some of the worst despots in history.
Certainly you can be a law-abiding citizen in human society apart from Biblical moral values. In that regard you have accepted society's standards as your moral values.
Why many reject Biblical moral values is because they encompass sexual relationships and conduct. It's perfectly legal in our society to live with someone outside of marriage and even have kids together. In fact, there was this reality show called "All My Babies' Mamas" that almost made it to air where this guy has 11 kids by 10 different women. It's all perfectly legal as long as he provides for those kids. As a Christian I consider that immoral, but you may not.
Speaking of cherry picking, you are cherry picking your own Bible. You are ignoring the messages of slavery, sexism, genocide, murder, and rape exercised and/or endorsed by your God.
