People either love or hate abstract painting.
As an artist I find it very liberating. It's like music without words. The colours create harmonies, ebb and flow and can be very evocative.
They can convey an emotion without grounding it to a particular instance. Anger can be demonstrated without showing a particular face, serenity without a place. It allows the viewer to become engaged on a much more personal level without the artists reality getting in the way.
I like to think that there is an abstract painting out there that will speak to anyone who thinks they don't like abstract art and bring about that "eureka" moment.