According to textbook and wikipedia, "if income elasticity of demand of a commodity is less than 1, it is a necessity good. If the elasticity of demand is greater than 1, it is a luxury good or a superior good."
Why was 1 chosen as the threshold?
I think that luxury good is consumed in larger proportion by relatively rich people. How does income elasticity of demand is greater than 1 reflect this?
As for your first question: income elasticity of demand is just a percentage change in quantity demanded divided by a percentage change in demand. If you divide two things that are equal you get one: $\frac{a}{b}=1 \iff a=b$ (as long as $b \neq 0$). Same thing goes for income elasticity of demand, $1$ is not just some random value that was chosen to separate between goods. When $\%\Delta$ in quantity demanded is greater than $\%\Delta$ in income, then $\mathrm{YED}>1$ just as in terms of letters $a$ and $b$: $\frac{a}{b}>1 \iff a>b$ (as long as $b > 0$).
As for the second question: income elasticity of demand that is greater than one can be translated to "as the income grows, proportionally more is spent on luxuries". Which is exactly what you have in mind.
