There are people who believe that God cannot exist without objective morality, but objective morality doesn’t need God. We can follow objective morality (assuming anyone can figure out what it is) without caring about whether some higher being exists or not. There are also people who believe in subjective morality, and that doesn’t exclude the existence of God but does imply that most of what typical Christians believe about him would be wrong if he did exist.
There are also people who don’t believe in “morality”, finding it arbitrary and incoherent, so instead go with “ethics”. Which is what works as a practical matter, regardless of whether other people believe it is right or wrong. Admittedly, that requires there to be agreed-upon goals; and for most people who pursue ethics, the primary goal is making a maximally-functional civilization, and the secondary is minimizing suffering and/or maximizing pleasure and fulfillment. Also admittedly, that’s still arbitrary on a different level, but there’s a fundamental difference - ethics are discovered and refined, while morality is declared. A person pursuing ethics says “we can probably do better than this, but it’s useful in the meantime” while a person pursuing morality says “this is the best which can be done, no one should ever do anything else”.
Also, people who call your father a liar do so because, regardless of their beliefs in ethics and/or morality, “liar” has a dictionary definition and your father very much is one. It’s not necessarily moral outrage but a statement of fact, and even when it is, not everyone saying that is an atheist.