The size of the parent star is crucial for the ability of that star to support life.
Stars increase in luminosity as they age.
For stars larger than our Sun, the increase in luminosity is much greater, which could not be compensated. Stars smaller than our Sun are not suitable to support life on planets. Although these stars are able to undergo quite stabile burning for billions of years, their small mass requires that life-containing planets be much closer to the star. For example, both Mercury and Venus have rotational periods that are as long or longer than their revolutionary period.