If you actually examine the legal issues in depth, it's way more complicated and nuanced that what you imply; that simplifies the problem to the point of falsehood. Something that the Obama administration has actually flat-out said (or "admitted", if you prefer), albeit not to anywhere near the media blitz of the accusations, when they said they need a year to look at the issues involved with closure, because it's not a simple, obvious problem after all.
As a for instance... why would "avoiding US constitutional law" matter when it doesn't cover the detainees anyhow, as the Constitution only really covers citizens? You might be able to spin an argument about penumbric emanations or build an ethical argument of some kind out of that, but you certainly aren't going to get a straightforward argument out of the actual text of the constitution. There's been a lot of very careless assumptions about what the US Constitution and the Geneva convention contain tossed around on this issue, and on the whole I've found the debate almost entirely disconnected from reality in these past years.
You are free to "not like it" or think it is immoral, but its actual illegality is way murkier than the disinformation campaign has conveyed, to the point that it may not be actually illegal at all. Moreover, the moral and ethical issues haven't gotten a fair hearing either as the conditions have been routinely grossly misrepresented, to the point that almost universally when somebody actually goes there and visits it they expressed surprised at the way it really was. I totally believe that there are those who would consider the reality immoral or unpleasant, but very few people are actually operating off of a realistic view of the problem.
The real takeaway is that the situation is complicated, and when somebody says "the situation is complicated" and you have a hard time resisting calling that person a Nazi... hello! Wake up! That's a sign you're running on propaganda, not rational thought.