Here’s the three-sentence answer that your professor should have given: Start off by assuming that 0 < x < 1, and multiply all three numbers by x. Then you see that 0 < x^2 < x. That’s why numbers between 0 and 1 get smaller when you square them.
Right on. That is such a clear and simple explanation, I’m ready to prematurely declare it the best.
The one thing I’d take care to explicitly emphasize, though it’s already implicit in that explanation, is that this is just a special case of the fact that multiplying anything by a number between 0 and 1 makes it smaller. That is, I’d note that this doesn’t really have anything to do with squaring in particular; squaring just happens to be one particular case of multiplication.