Summary
Mew is a rare Pokémon with great psychic power, the genetic ancestor of all Pokémon and the basis for Mewtwo. Mew is depicted as a force of nature, detached from humanity and indifferent to human values. Mew's personality was intentionally created to be erratic, representing nature and contrasting with Mewtwo's human origins.
Legendary Pokémon are incredibly rare and special species, in both the games and the anime. Few are more iconic than Mew, the original Legendary Pokémon, and the Pokémon anime director has confirmed how they captured the elusive creature's traits when it came time for Mew to make his anime debut in Mewtwo Strikes Back.
In-universe, Mew is an extremely rare Pokémon that possesses immense psychic powers and is believed to be the genetic ancestor of all Pokémon, allowing it to use a wide variety of attacks. Mew's DNA also served as the basis for the creation of Mewtwo, the star of the aforementioned first Pokémon movie. Mew almost had to appear in such a film due to their close relationship, but little is decidedly known about Mew at this early point in the series.
So when it came time to flesh out Mew's personality and behavior, the anime team decided to make it as different as possible from Mewtwo.
Mew is a Pokémon with the power of nature.
Mew's power sets it apart from humanity.
In a 2023 interview with director Kunihiko Yuyama, translated by Serebii.net forum moderator Dephender, Yuyama was asked about how they developed the characters Mew and Mewtwo for the original film. Yuyama immediately describes Mew as “a transcendent being that exists beyond human values of right and wrong”. He goes on to explain that, like the ocean or the mountains, this beautiful thing can also be terrifying and dangerous at any moment. Mew is said to be a capricious representation of nature, in contrast to Mewtwo's human origins.
This fits well with Mew's depiction in the show; while it's often curious about humans and what they're doing, it's also easy to entertain itself, and it seems to think nothing of it when it comes to Mewtwo. Even when Ash is turned to stone by their fight, Mew is initially quite confused, until it sees the other Pokémon start to mourn. If that hadn't happened, Mew would probably have been perfectly fine with letting Ash continue to fight his twisted fate.
This could also explain why Mew does not speak, while Mewtwo does (at least telepathically). Mew does not consider humans special, and does not see any real need to communicate with them, so it simply does not communicate. Mew is capable of communicating with Ash and his friends, but it simply chooses not to. Since Mew has no concept of human morality, this could make Mew come off as cruel and heartless, which contrasts greatly with its cute appearance.
In that sense, Mew's status as a Legendary makes it akin to a god, a powerful being that exists far beyond the boundaries of human morality and philosophy. While some later Legendary Pokémon have taken the status of a god literally, this proves that even back in Mew's time, Legendary Pokémon were viewed that way by the creators behind the anime. Mew is more than just a human, and perhaps even more than a Pokémon.