Is there a sound doctrine or biblical explanation why Satan is called the “Ape of God”?
The Adversary, in waging war against the Almighty, is understood to copy all of his acts and attributes. Popular tradition, moreover, asserts that the Devil, impotent to do anything original, has set his heart on aping
everything created by the Deity.
Tertullian was led to declare that "Satan imitates the sacraments of God" and "goes about to apply to the worship of the idols those very things of which the administration of Christ's sacraments consists.”
Tertullian has already said that the Devil, as the ape of the Deity, practices baptism on his subjects. - DIABOLUS SIMIA DEI
St. Augustine of Hippo says this about the ”Ape of God”:
Dr. Farr says, “In Eph. 5:18, two possible sources of simulation are indicated - drunkenness and Deity; full of wine or full of the Spirit. Satan was called by Augustine Simius Dei, the Ape of God, because he counterfeits the work of God. Human nature needs a stimulus of some kind. Doubtless, the Holy Spirit was intended to be the only original stimulus of humanity, but Satan invented alcohol as a substitute, stealing the nomenclature of the truth to mask the lie, i.e., Aqua vitae, eau de vie.” - Outline Studies in Christian Doctrine
The Encyclopedia Britannica adds the following:
Among the early Church Fathers, the idea of Satan as the antagonist of Christ led to a mythical interpretation of the incarnation and disguise in the “form of a servant.” Through this disguise the Son of God makes his heavenly origin unrecognizable to Satan. In some medieval depictions Christ appears as the “bait” cast before Satan, after which Satan grasps because he believes Christ to be an ordinary human being subject to his power. In the Middle Ages a further feature was added: the understanding of the Devil as the “ape of God,” who attempts to imitate God through spurious, malicious creations that he interpolates for, or opposes to, the divine creations.
St. Augustine actually liked comparing the Devil to animals, as it is something our imaginations can understand.
The saints have their own specific way that they name or describe the devil and each description manifests a different dimension of the evil of the devil himself. St. Augustine also calls him an angry dog bound to a chain.
He (the devil) is tied up like a dog on a chain, and can only bite someone who, deathly sure of himself, goes near him. Wouldn’t you think a man a fool who let hiimself be bitten by a chained up dog?
He can only bite those who willingly let him. It is not by force, but by persuasion, that he harms: he asks for our consent, he does not drag it from us. - Augustine on the binding of the devil
Finally, the Prince of the Apostles, St Peter calls the devil “a roaring lion seeking whom he can devour…” This Biblical name as well as names that the saints have coined for us can help us to understand the malicious intent of the devil!