Am very glad that your son is OK and that it was nothing serious. But, air carriers on long-hauls have to look at it exactly the opposite way. Same thing as hospitals which treat stomach upset as a heart attack until the more serious condition can be ruled out. Unfortunately vomiting and dehydration at high altitude can be a lethal combination and while aircraft can make emergency landings, that actually can be very risky when aircraft are too heavy due to the fuel they are carrying for the long haul.

If you were at origin or destination and your son became ill, would you have flown without a full examination by a physician? I suspect not and that's what Emirates faced. While it's possible that they overstated the volume of the condition (to be polite), the fact of the condition alone is scary.

As to rebooking on another carrier, I very much doubt that any carrier would purchase a ticket for a pax in this situation on another carrier. Again, had your son become ill at the departure airport, the right thing to have done would have been to rebook you on the next available online flight. The same is true for this situation.

All of this seems terribly unfair in the instant, but looking at it as one must from the bigger picture, the inconvenience of delay is far outweighed by the risk of flying at high altitude over long distances.

There are other threads posted by people in casts or far along in a pregnancy. The calculus is still the same.

If I were in your shoes, I too would have been furious in the instant. But, upon reflection, I would be grateful that someone else made this decision for me.