Betta don't have teeth, and the food that they are fed is much different, and harder, then the food they eat in the wild, so they spit it out repeatedly to soften it up. This is common behavior in pet bettas.
If the type of food you are feeding it is not too big, then there can be a number or reasons. Bettas can be partial to certain food so try changing its diet. In addition, check to make sure you are not overfeeding the fish. It can also be a sick and can't bear to eat.
I've seen many of them do that. Have you ever sucked the sweetness out of a popsicle. I think it is something similar. I don't think they are rejecting it, but they just don't want it all (being fussy). Fish food is quite tricky sometimes. As long as he doesn't get skinny don't worry.
Beta fish are picky eaters. Try feeding your fish either freeze dried bloodworms or freeze dried brine shrimp. It also could be that the food is too big. Your fish might be spitting the food out in order to break it into smaller pieces.