The justice system isn't for only doing what is just at all times, it is for enforcing the consequences of laws.
The point of a law is simply to put down the rules by which order is maintained, and that order is dictated by the morality of the majority of people who hold power in government. The justice system merely upholds the law set down and doles out what the law defines as a 'just' punishment or judgment.
A law can say literally anything, like, "Black people may not marry White people", or "Women may not vote", "Gay people may not get married", etc. Or they can say things like "At an intersection, the left-most lane may turn left onto the street it intersects with, but not the right-most lane." It can say anything; it doesn't have to do with "fairness" and "justice", it has to do with maintaining order.
The laws, once put down, are enforced, as long as they remain laws. The results of those laws being enforced will only stop once the laws are abolished (and even then, sometimes the states just like to keep going with 'em even if they've been abolished anyway).
We can't just selectively enforce or not enforce laws. Then there would be no point to the law. Then literally any local government official, judge, court, president, etc could abuse the rights of citizens or allow people to go free simply because they felt like it. And that's not in the public interest.
Therefore, laws which are deemed to be unfair or unjust must be amended or abolished. But - and this is the important part - they must simply be made by decree by will of the representatives of the public, and must not always meet a measurement of justice or fairness. Not only because there are plenty of laws which simply define what the proper procedures of daily life are, but because we'd literally never get any laws passed if we had to have a philosophical discussion about the potential pros and cons of the impact of the law on justice as a general idea.
So why are they forcing him to make an unfair choice? Laws aren't designed to be fair. Only the consequence of the law can be fair, according to that law. In this case, if you ask a guy if he wants to live, and he says, "No", is it fair to give him death, assuming he was of sound mind and body and understood the consequences of his decision?
Yeah.