A.M.
Due to the fact that your son was born prematurely there is a good chance that he has some decreased oral motor skills. He may have a difficult time eating table food because he may not have the ability to move his tongue around in his mouth to aid in eating and his jaw strength may be weak which would make chewing up the food difficult. Meat is generally one of the more difficult things to eat due to the amount of chewing involved.
Your son may also have some tactile defensiveness and avoid certain textures of foods. Your son may or may not have other signs of tactile defensiveness like difficulty with having someone brush his teeth, wash and cut his hair, cut his nails, etc...
I would recommend taking your child to an occupational therapist in order to have them evaluate your child's eating. They can determine if your child's oral motor skills are age appropriate or if he is defensive to certain textures. If either of those things are a problem they can be treated. Hang in there.