Kṛṣṇa - A Viṣṇu Avatāra?

Some time ago, I came across a subtle meme on the internet which comprised of a painting of Lord Kṛṣṇa and was captioned, “Kṛṣṇa – used to be the eighth avatāra of Viṣṇu.” The meme was subtly trying to mock those who claim that Kṛṣṇa isn’t just an avatāra (incarnation) but the avatārī (source of all incarnations) Himself. For a long time, Hindus have believed that Kṛṣṇa is the eighth avatāra of Viṣṇu, and the idea that He is instead the source of Viṣṇu Himself sounds like a modern-day invention to them. Why do Hindus think like this? If Kṛṣṇa really is the Original Supreme Personality of Godhead, then how did this idea that He is an avatāra of Viṣṇu creep into the minds of almost all Hindus? In this write-up, I will try to answer this question while also explaining why exactly the Hindu idea that Kṛṣṇa is an avatāra of Viṣṇu is incorrect.