One Isis horror story goes like this. Isis members raped a mother in front of her children. She was crying and screaming while being raped. The one of the Isis persons beheaded her baby in front of her and placed the baby on her lap.
Call this example X. Write X into a moral claim: X is wrong.
Is X objectively wrong? If so, then the claim X is wrong is true for everyone, just as I'm now typing these words is true for everyone.
Many believe that if God does not exist then there are no objective moral values. On atheism X is wrong is not an objective claim; viz., it is not true for everyone.
It's not hard to find intellectual atheists who believe that God and objective morality stand or fall together. That is, who believe that if God does not exist, then objective moral values do not exist. Here are some examples.
Jean-Paul Sartre: “It [is] very distressing that God does not exist, because all possibility of finding values in a heaven of ideas disappears along with Him.” (Sartre, Existentialism and Human Emotion, 22)
Friedrich Nietzsche: “There are altogether no moral facts”; indeed, morality “has truth only if God is the truth— it stands or falls with faith in God.” (Nietzsche, Twilight of the Idols and the Antichrist, 55, 70)
Bertrand Russell rejected moral realism and retained the depressing view that humanity with all its achievements is nothing “but the outcome of accidental collocations of atoms”; so we must safely build our lives on “the firm foundation of unyielding despair.” (Russell, "A Free Man's Worship," in Mysticism and Logic and Other Essays, 41)
J. L. Mackie: “Moral properties constitute so odd a cluster of properties and relations that they are most unlikely to have arisen in the ordinary course of events without an all-powerful all-powerful god to create them.” (Mackie, The Miracle of Theism, 115)
Richard Dawkins concludes that a universe of “just electrons and selfish genes” would mean “there is, at bottom, no design, no purpose, no evil and no good, nothing but blind pitiless indifference.” (Dawkins, River Out of Eden: A Darwinian View of Life, 132-133)
Because real atheism is philosophical naturalism, and nature (matter) is valueless, "Why think that value would emerge from valuelessness?" (Paul Copan, "Ethics Needs God," in Debating Christian Theism, 86)
The atheist who, e.g., accuses Christians of being "intellectually dishonest" tacitly assumes the existence of God, without which his moral accusation is logically incoherent. Such an "atheist" is precisely the despicable "village atheist" Nietzsche writes about.