It's partly inherent in the way things scale.
If you double the length of the model, then the wing area (length times width) increases by a factor of 4, but the weight and volume (length times width times height) will increase by a factor of 8 ... so doubling the size means halving the weight-to-lift ratio.
In the most extreme cases, a tiny model will blow away on a puff of wind, and a huge model (bigger than the real plane) can't take off at all.
I suppose you might theoretically try to make small models harder to fly, by adding extra weight.
The above is theoretically true but maybe nonsense in practice: it assumes that structural materials become thinner when the model is scaled, in reality the structure isn't even the same material.
So let's look at it another way:
A full-scale A380 weighs let's say 500 tons, length about 70 metres.
Decrease that to 1 metre model and the surface area has decreased by (70x70=) 5000.
So for the model to have the same weight-to-area as the full-scale plane, it would need to weigh (500 tons / 5000 =) 100 kg.
Your 1 metre model presumably weighs much less than 100 kg, therefore it has much less weight-to-area ratio. QED.
It's also important to consider the Reynolds number, which depends on the air's viscosity and density, and on the size and speed of the model. The Reynolds number affects turbulence, which is very important to a wing's lift (for an example of how even a tiny change has a large effect, see Can a sandpaper-thick layer of ice reduce lift by 30 percent and increase drag up to 40 percent?).
To get the right Reynolds number for a small model you must increase the density (e.g. pressure) of the air, or increase its speed. But given the ordinary speed of aircraft, you couldn't increase (scale up) the air speed because it would become super-sonic, which would change the scenario.
Based on this answer to 'Understanding the Reynolds-number scaling problem', and the comments below it, I think that a 1-metre model of a 70-metre A380 (so a scale of 70:1) might behave like the full-scale model if it were flown under the following conditions:
- air density is scaled up, so 70 atmospheres of air pressure
- lift and drag are scaled down, so:
- weight of the model is 7 tons (instead of 500 tons)
- thrust of the model is 4,000 lb (instead of 300,000 lbs), i.e. about 2 tons
- air speed is realistic (e.g. 150 knots to take off)
Obviously this would be quite unusual for a model airplane1.
1Air liquifies at 60 atmospheres; and the model would need a specific density of about 100, i.e. 5 times heavier than gold or uranium).