It causes a number of problems. A planet that's tidally locked will experience bizarre weather conditions, and of course, one whole side of the planet will
never receive any light. This would preclude photosynthesis on the night side.
While the atmosphere will keep the night side relatively warm (assuming the planet is close enough to its star to have liquid water), the night side will constantly be swept with fierce winds, toward the solar pole. Additionally, the night side will experience perpetual torrential downpours at the solar pole.
More importantly though, most of the energy released by red dwarf stars is in the infrared range. The "day side" wouldn't exactly be bright. Red dwarfs are also much more unstable in their energy output than our main sequence star is.
It's absolutely possible that life could exist on a tidally-locked planet orbiting a red dwarf star, even carbon-based life. But it would be radically different than life on our own planet... for instance, all plant life on a planet with a red sun would be
black to our eyes, in order to maximize absorption of infrared energy. Very alien indeed. And while
humans could possibly live on these worlds, it would still be a very hostile environment (though less so than deep space or an atmosphere-less chunk of rock) and much technological measures would be required to maintain our bases and habitats.
Now, if we step away from our arrogant presumption that all life must be carbon-based and must require water, the possibility of other planets supporting life increases substantially... just not
our lives.
