I'm a simple man living his life and enjoying mathematics. Today while thinking about choices I realized this paradox:
If I have $2$ choices and $1$ of them is taken away, I have $0$ choices.
How is that possible? Simple math shows I had $2$ choices, I took $1$ away, and I'm no longer left with any choices because there is nothing to choose...
On
You are abusing the word "choice," giving it two meanings.
You have one question (What to eat?) with two options (hot dog or hamburger.)
To be a "choice," a question has to have to have at least two options. So when you reduce the options by one, you no longer have any choices.
By applying the word "choice" to both the question ("What do I eat?") and the options ("burger," "hot dog") it is not actually surprising that reducing your choices/options from two to one reduces your choices/questions from one to zero.
You could make a dual "joke" with the same error, but in the other direction:
Why is it that, when I start out with two choices, and I make one choice, I have no choices left?
If you have $2$ balls, then there are $2$ ways to choose $1$ ball out of the $2$.
If you have $1$ ball, then there is $1$ way to choose $1$ ball out of the $1$.
These correspond to the binomial coefficients $\binom{2}{1}$ and $\binom{1}{1}$ respectively. This is how we think of the matter mathematically.