Hello and thank you for visiting JA.
I think the first thing you should know is that he will not starve himself into illness, and secondly that it is not worth getting into fights over.
What you are experiencing is a worriesome but very common phase which many children go through inone way or another.
From a psychological standpoint this is seen variously as a means of beginning to exercise real choice, as ameans of asserting independence or as an anxiety
based call for attention.
Make sure that you check his weight and height regularly, and so long as it stays within acceptable limits, he'll be doing fine. You can do that by using the Body Mass Index Calculator you will find here:
There is also some excellent help here:
Don't try to force him, take it calm;ly, and let him pass through this phase, unless it continues over a period of more than 6 weeks, in which case, he would best be seen by a pediatric psychiatrist.