Answer
This is (literally) a hands-on demonstration. Try it and see!
Our brains sometimes overrules our eyes, and vice versa. Another "angular size" illusion that can be hard to believe is that the moon is the same size whether it is high in the night sky or down low near the horizon. You can exactly cover the moon with an appropriately-sized object held at arm's length in both cases, but most people will swear that the moon is larger when it is low in the sky.
