Pigs with feed preferences will eat at least one type of feed.
They'll get annoyed if you try to feed them something they don't like - figure out the feed at which they didn't get annoyed.
If that still doesn't seem to work, try loading a different area (such as the Pig Center), reload the Pig Pen and see if that fixes the problem.
Further, if the hunger gauge is yellow, your pig is full and will not eat anything. Wait until the gauge changes color.
Note that pigs will not eat feed while the App is closed, even if you leave feed in the Pig Pen.