There is a "frost line" in the middle of the asteroid belt where you see rocky objects closer and icy objects further. The reason is that closer the Sun has enough energy to sublimate the icy objects into a comet with a tail, where the tail is the icy material being blown off into space. Over billions of years that results in objects with ice-free rocky surfaces inside the frost line, and big, gaseous, volatile-rich outer solar system objects.

So at the time of the formation of the solar system, the whole area was a big gaseous cloud of supernova debris with lots of ice. The ignition of the sun started the frost line, and pushed volatiles out of the inner solar system. However some had already been trapped in the formation of the planets, and rose to the surface as they cooled. That's where Earth's ocean came from, and we know Mars and Venus had oceans too. Presumably also Mercury, although I'm sure that was short-lived.

So yes, it's all from cometary material. But then ALL of the Earth is from cometary material, and the oceans only make up a small amount of the Earth's total mass.

> Why couldn't the Earth have formed with its own water?

We’re not sure from where Earth’s water came [1]. Some evidence suggests the Earth was born with all its water, some that most came from comets.

[1] https://en.m.wikipedia.org/wiki/Origin_of_water_on_Earth

Earth likely had some water during early creation (accretion) but the best theory on how the Moon formed is that a Mars sized object hit the early Earth at the end of accretion. This blasted much of the Earth's rock part (mantle) and any water it might have had into orbit. The rock part quickly fell back to Earth and the rest condensed and collapsed to form the moon. The water and other volatilizes that were on Earth were blown away by the solar wind at that time. The surface of the Earth and Moon would have been boiling lava at this point and had to accumulate water from new impacts of comets and icy asteroids.

The water on Earth may seem to be a lot to us on the surface but it is only about 0.02% by mass [1].

https://www.universetoday.com/65588/what-percent-of-earth-is...

There's actually a lot of water in the mantle of the Earth. There's something like 3x the current ocean volume trapped in the mantle, and there are theories that pressure differentials cause this water to escape as gaseous water escapes from the atmosphere. It would explain why the ocean happens to be approximately the height of the continental shelf, and always has been. Under this theory the water simply emerged as the Earth cooled from the impact. The Moon, on the other hand, would be missing this water as the debris was mostly stripped of water content as it accreted.