You don't really need a physics paper to explain it to him. For the sake of this conversation, this applies to flashlights with just reflectors right (no special lenses).
The physics is really simple:
1. Light is reflected (duh).
2. In order to get perfect throw, you must have the light rays leave the flashlight parallel to each other (perfect collimation).
3. Light always obeys the law of reflection (the angle of incident light always equals the angle of the reflected light against a normal surface)
4. So in order to get collimation, you must always have a specific shape (angles must be met). Only a parabolic reflector can do this.
5. A larger reflector therefore gathers more light and therefore produces more throw.
You can imagine that a 1cm reflector will miss a whole lot of light vs one that is say 10cm (remember both have to be the same shape to produce collimation). This means that shorter reflectors can be thought of as basically larger reflectors that have been "cut down" from the front.
Both reflectors MUST meet this light at a specific angle, and since the reflector is one piece, you cannot design a smaller reflector that possesses the same characteristics (say, if you try to make it smaller, you'll sacrifice collimation near the LED). You cannot make a smaller reflector that has all of its surface parallel to the "perfect" reflector shape and collect the same/more amount of light.
The above depicts a perfect light source (point) and a perfect reflector. Of course LEDs are not point sources. This allows flashlight makers to divert slightly from the "perfect" shape since an LED is essentially multiple point sources. So you can sacrifice angles (and therefore collimation) near the LED without a huge loss (but there is loss!), but nonetheless, the same principle still generally applies (you still would collect more light and more collimation from larger reflectors).
Conversely, this can be used to explain why larger LED dies exhibit floody characteristics. A Cree XM-L, although brighter, can generally be outhrown by it's XT-E/XP-G brethren. This is because the larger die size of the XM-L makes it harder (actually impossible) to achieve the same degree of collimation as smaller die sizes. A reflector with an XM-L will not be able to meet all of the light rays at the correct angle, therefore, it tends to be floody. This is even more exaggerated in smaller reflectors.