As previously mentioned, evolution isn't always about the best solution, but instead can be the result of simply being the first. Even if an organism is less effective, if it can secure a large enough foothold before other organisms, then it is incredibly difficult to displace them. But I have a couple of other reasons that this might be.
The atmosphere of the planet somehow filters out red and blue light, necessitating a different pigment choice.
A mutation caused a plant to become unable to produce chlorophyll but simultaneously added a different trait that made it more successful thus overriding that detriment. (Many plants have secondary photosynthetic pigments, so this would not necessarily mean doom for the plant.)
Your planet receives an inordinately large amount of sunlight. Chlorophyll is better in lowlight environments, but it has no distinct advantage over other pigments in extremely sunny environments.
While not specifically for cyan colored plant life if you also want red foliage you can have your plants use phycoerythrin as their photosynthetic pigment. This is the pigment that gives red algae their coloration. If you want cyan plants, then as previously mentioned phycocyanin is your ticket. You might also look into what is being done in artificial photosynthesis research, as that may lead to some novel pigments that nature simply would not have come up with.
An interesting note with plants, they can survive a much greater degree of mutation in their DNA than animals can, so having your plants mutated by something as extreme as a solar flare is not out of the question.
Hope something in this helps.