The trouble is the loss of water to space.
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On smaller bodies, this loss is greater, and there might not be any water left, only the evidence of it being there in the past.
Mars seems to have only a bit of dense CO2 left, whereas Jupiter's mass still retains even methane.
The body's temperature also plays a role in this loss rate.
That does indeed play a role. Mars dried out because it was smaller, cooled faster than the Earth, and lost it's magnetic field from it's once molten core, which allows the solar wind to strip atmosphere. UV light from the sun splits H2O and the hydrogen escapes to space.
OTOH, even smaller bodies, largely protected by ice, like the gas giants moons, such as Europa have more liquid water inside than all the surface water on Earth. Protected from space by the ice, and the core is continually tidally squeezed by the parent planet's large gravitational field, generating heat indefinitely. And it's unclear even here on Earth if life started on the surface in places like tidal pools, or if it started at the bottom of the ocean around geothermal vents. If it started at the bottom of the ocean, sunlight might not even be a prerequisite.
Liquid water is a strong indicator of the
potential of life, because at the temperature range of liquid water, and with carbon compounds, the chemistry is complex enough to support life. It does not automatically equal life, but it's a huge, if not the biggest prerequisite. And in typical journalistic hyperbole, the scientist excited that water enhances the possibility of finding life, it gets blown up into "water=aliens!" etc. by the journalist.
Others will go on about other potential chemistries like silicon, or in the liquid methane/ethane oceans of Titan, and that water/carbon is just an Earthly conceit based on confirmation bias. However, as our understanding of chemistry has grown, it's becoming more and more clear that the number of potential chemical combinations is much much lower, and the rates of formation (and destruction) of compounds/molecules is either too slow, or too high in other environments that are too cold, or too hot for liquid water.
Liquid water and carbon is the "sweet spot" in the Periodic Table where all the interesting stuff happens. We find that space is lousy with amino acids and other organic molecules, but without liquid water and the temperature range and pressure that supports it, they'll just sit there and do nothing.
And in terms of non-carbon chemistry, you're never going to get some analogue to RNA or DNA, or the complex array of protein synthesis from silicon in... I dunno, lava or whatever as an alternate working fluid.
