Cycling has carbon emissions if you factor the additional calorie intake needed to power your bike. :| Which will vary widely depending on your size, diet, and food source. Is it still a more sustainable form of transportation? Probably, but maybe not in extreme cases (like a 300-lb person eating beef daily flown in from the other side of the planet, versus, a tiny two seater electric car power off of solar energy, using batteries sourced from recycled materials) and it certainly isn’t 0 impact.
Also, for extra pedantism, carbon emission are not pollution (in the sense that it doesn’t poison the life forms directly), but it is a GHG which causes harm to the environment too.