Water on Mars and Earth

The loss of liquid water on Mars was also due to the planet losing its magnetosphere. During the Hesperian period (about 3500 mya) the iron core stopped rotating fast enough to create a planet-wide magnetic field of the type Earth has. Because of this, the Martian atmosphere was no longer protected from solar wind, which caused it to erode away to its current (very low) density. Without enough gases in the atmosphere to generate a greenhouse effect, Mars became much colder and drier. This is why there's no liquid water on its surface at present.

If water on Earth came from meteorites, why doesn't Mars have substantial water?

First off, that's a conjecture regarding the origin of the Earth's water rather than a known fact. A few times a year or so, a new journal article will appear that argues that the Earth's water is primordial, then another arguing that it came from comets, then yet another arguing that it came from asteroids.

If the Earth's water is mostly primordial, most of it is over 4.5 billion years old. If it came from asteroids or comets that collided with the Earth after the Earth had formed, it's still very, very old. Regardless of the source, almost all of the Earth's water has been here for at least 3.8 billion years old, since the end of the late heavy bombardment.

The same would apply to Mars. It has had almost four billion years to lose its water. So has the Earth; some argue that the Earth, too, has lost a lot of water to space in those four billion years.

The key causes of the disparity is that the Earth is significantly more massive and has a magnetic field. Mars's essentially non-existent magnetic field means that water molecules in the atmosphere are more readily split into hydrogen and oxygen than are water molecules in the Earth's atmosphere. Mars's smaller gravitational field means the hydrogen produced by these events has a much greater chance of escaping before it re-forms water than on the Earth.

A very recent conjecture poses another possibility, which is that Mar's mantle is slightly different in composition than the Earth's, and this different composition enabled Mars's mantle rocks to absorb significantly more water than did the Earth's.

Mars did have a significant amount of water (and atmosphere) early in its history. According to NASA, there was enough to form an ocean covering about half its surface: https://www.nasa.gov/press/2015/march/nasa-research-suggests-mars-once-had-more-water-than-earth-s-arctic-ocean/

The reason it doesn't have a lot of water or atmosphere today is that much of it evaporated, essentially because of Mars' smaller size and lower gravity.