I do not think this is what your saying but bare with me, I have to pose the question. Do you think there is no rational argument for these rights?
I believe there are rational arguments for them and I believe that the rational arguments for them are better than that against.
However, I think there are rational arguments against. For example, if we all lived regimented lives, where we were compelled to eat some specific diet, we may well, on the average, live longer. If I bring up that certain people have certain special needs, than the person supporting regimented diet can say that specific, regimented diets can be made for specific needs.
I'd just as soon skip to the chase: As part of my right to pursue happiness, I have the right to eat what I can afford to eat. Maybe I will live a shorter time because of it, but I will enjoy that time more. I cannot rationally demonstrate that -- after all, how do you rationally demonstrate "higher enjoyment"? -- so I appeal back to the authority of the Declaration of Independence for my argument.