My son grew up eating spaghetti, spaghetti o's, loads of peanut butter, pancakes, bean taco's or burritos, green beans, applesauce, chicken noodle soup, boiled eggs and yet more peanut butter. He was a skinny child but healthy. The doctor said he was fine because he did eat peanut butter and beans. Those are good proteins. This lasted until about the age of seven.
I did not have the luxury of the internet in researching good meals and proteins to give him in lieu of meats at that time. I would suggest you do the researching and not push your child. As my son grew older he became only a meat eater until the age of 22. That was hard as he only wanted meat and no veggies.
Now he is 30 and eats most anything his wife puts in front of him except onions. He is healthy and actually fighting some of his weight for the first time ever.
Again do not push your son. Talk with a doctor and research on the internet. It is a preference of his and could be something his body is telling him that he does not know or understand. Example: My son had IBS and his body could not handle big meals until he grew older and understood how his food reacted with his system. We did not know he had the problem of IBS back then. Just something we put up with if he was constipated or had diarrea.
Another good thing to try is have your son help you with his meal. I know he is young but offer him to grab the spoon, cup, napkin etc.. to help you. Later on as he ages let him choose his meal, stir items, set the table, clear the table, get things from the refrigerator and even later help cook. This helped my son feel like he had choices and he ate better.
Good Luck in your issue with your son. I hope some of this information has helped you. Remember to stay positive and do not get stressed unless you are given a reason to stress. Mothers have enough gray hair without getting them too early. LOL
God Bless!