I have a very hard time getting my son, a kindergartner, to eat breakfast before school. I have tried everything I can think of to entice him to eat: nontraditional breakfast foods, cold foods, hot foods, etc. I can only get him to eat a few bites of food and he refuses to eat more, even though I've explained how important it is for his body and his brain to have fuel to learn and play all morning before lunch. When he's not hungry, he just won't eat! How important is it to eat a full breakfast? Can he get by on a few bites?
This is one of those situations where you just have to trust that your child's own body will tell him what to do. Assuming that your child is a normal child who has had normal growth and development up until this point, this is a battle that you won't win. You cannot force him to eat if he is not hungry. However, you also don't want to give in to him by offering him junk foods or foods that you don't approve of just to get him to eat something. Most people do need something in the morning in order to give them enough energy. However, there are some people who need only minimal amounts and who seem to function quite well. Since he is in kindergarten, I'm sure he is getting a mid-morning snack at school, so he goes only about two hours until he eats.
I would continue to offer him nutritious foods and allow him to eat until he is satisfied. If you know he is only going to eat a half bagel, then only make a half bagel for him and don't make an issue about him not taking anything more than that. You might want to talk to a nutritionist to get suggestions for high energy foods that he might like.