Here’s an article from Evolution News that talks about liquid water and tidal locking, but it has even more factors that need to be fine-tuned for habitability.
Stars with masses of 0.1-0.5 solar mass make up 75 percent of the stars in our Milky Way galaxy.6 These represent the red dwarfs, the M class. But these stars have low effective temperatures, and thus emit their peak radiation at longer wavelengths (red and near-infrared).7 They can have stable continuously habitable zones over long time scales, up to 10 billion years, barring other disruptions. It is also easier to detect terrestrial sized planets around them.8 But a serious problem with red dwarf stars in the K and M classes is their energetic flares and coronal mass ejection events. Potentially habitable planets need to orbit these stars closer, to be in these stars’ habitable zones. Yet the exposure to their stellar winds and more frequent and energetic flares becomes a serious issue for habitability. Because of these stars’ smaller mass, ejections get released with more violence.9 Any planet’s atmosphere would be subject to this ionizing radiation, and likely expose any surface life to much more damaging radiation.10 The loss of atmospheres in these conditions is likely, but the timescales are dependent on several factors including the planet’s mass, the extent of its atmosphere, the distance from the parent star, and the strength of the planet’s magnetic field.11 To protect its atmosphere for a long period, like billions of years, a planet with more mass and thus higher gravity could hold on to the gases better. But this larger planet would then hold on to lighter gases, like hydrogen and helium, and prevent an atmosphere similar to Earth’s from forming.12 Another consequence is that the increased surface pressure would prevent water from being in the liquid phase.13
So again, you need to have a huge, massive star in order to hold the planet in orbit over LONG distances. If it’s a short distance, you not only have the tidal-locking problem, but you also have this solar activity problem (flares, coronal ejections).
But wait! There’s more:
Another stellar parameter for advanced life has to do with UV (ultra-violet) radiation. The life-support star must provide just enough UV radiation, but not too much. UV radiation’s negative effects on DNA are well known, and any life support body must be able to sustain an atmosphere to shield them. Yet the energy from UV radiation is also needed for biochemical reactions. So life needs enough UV radiant to allow chemical reactions, but not so much as to destroy complex carbon molecules like DNA. Just this flux requirement alone requires the host star have a minimum stellar mass of 0.6 solar masses, and a maximum mass of 1.9 solar masses.14
So the ultra-violet radiation that is emitted has to be finely-tuned. (I’m guessing this assumes some sort of chemical origin-of-life scenario)
Another requirement for habitable planets is a strong magnetic field to prevent their atmosphere from being lost to the solar winds. Planets orbiting a red dwarf star are also more affected by the star’s tidal effects, slowing the planet’s rotation rate. It is thought that strong magnetic fields are generated in part by the planet’s rotation.15 If the planet is tidally braked, then any potential for a significant magnetic field is likely to be seriously degraded. This will lead to loss of water and other gases from the planet’s atmosphere to the stellar winds.16 We see this in our solar system, where both Mercury and Venus, which orbit closer to the Sun than Earth, have very slow rotation rates, and very modest magnetic fields. Mercury has very little water, and surprisingly, neither does Venus. Even though Venus has a very dense atmosphere, it is very dry. This is due to UV radiation splitting the water molecules when they get high in the atmosphere, and then the hydrogen is lost to space, primarily, again, by solar wind.17
You have to hold on to your umbrella (atmosphere), or you get hit with dangerous rain (solar winds).
So a few more factors there, and remember, this is just the tip of the iceberg when it comes to circumstellar habitability constraints.