While the idea that the moon once belonged to Earth might be an interesting concept to entertain, I must assert that there is a wealth of scientific evidence which contradicts this view. Based on my understanding, there are three main areas where the Earth-moon relationship simply doesn't align with the notion that the moon used to be part of the Earth:

Different compositions: The Earth and moon have distinctly different chemical and isotopic compositions. The moon is significantly less dense than Earth and lacks certain key elements found on our planet, such as water and volatile compounds. This contradiction undermines the idea that the moon was once Earth, as one would expect the lunar body to share a similar average composition with the Earth.

Giant impact hypothesis: The prevailing scientific explanation for the formation of the moon is the Giant Impact Hypothesis. According to this theory, about 4.5 billion years ago, a massive celestial body the size of Mars, called Theia, collided with Earth. The debris ejected in that collision eventually coalesced into the moon orbiting our planet today. This explanation for the moon's origin points specifically to an external collision, rather than it being a part of Earth.

Similar age and timelines: Radiometric dating techniques have independently determined the ages of Earth and the moon to be around 4.6 and 4.5 billion years old, respectively. Given their close age, it would be nearly impossible for the moon to have once been part of the Earth without there being any evidence of a significant event that led to impact or fission.

Taking these scientific findings into account, it would be unreasonable to continue advocating the notion that the moon used to be part of the Earth. While fascinating from a speculative perspective, the available empirical evidence refutes such a claim