I've been looking at various ethics textbooks, and remembering why I don't really like ethics textbooks. Here is a good example from a textbook that, for the most part, is actually better than most you can find, Lewis Vaughn's Doing Ethics (5th Edition, W. W. Norton & Co., New York: 2019):
According to Aquinas, at the heart of the traditional theory is the notion that right actions are those that accord with the natural law--the moral principles that we can "read" clearly in the very structure of nature itself, including human nature. We can look into nature and somehow uncover moral standards because nature is a certain way: it is rationally ordered and teleological (goal-directed), with every part having its own purpose or end at which it naturally aims. From this notion about nature, traditional natural law theorists draw the following conclusion: How nature is reveals how it should be. The goals to which nature inclines reveal that we should embrace and the moral purposes to which we should aspire. (p. 139).
Literally every sentence in this paragraph is wrong, and not wrong in kinda-close-but-not-quite sort of way, either -- it is wholly wrong. The 'traditional natural law theory' that it imagines is entirely fictional.
(1) The first and most glaringly obvious mistake is the confusion about what 'natural law' means. Natural law is called 'natural law' because it is the law natural to human reason. The idea in Aquinas, and he is not atypical in this, is that there are certain principles of human reason that fit the definition of law, so law is not something that is merely made by us, it is something that is a part of reason itself. The paragraph above makes the common mistake made by beginners that 'natural law' in the sense used by natural law theorists has something to do with 'law of nature' in the sense of the stable course of natural actions and changes. It is in fact essential to natural law theory that this confusion not be made; 'law of nature' in the latter sense is a figurative sense of the term 'law', but in 'natural law' in the sense used in natural law theory, the term 'law' is used in a literal sense. What is more, natural law theory, as such, doesn't have anything to do with "the very structure of nature itself"; that is a matter of metaphysics, not natural law. And while there is a broad sense in which a natural law theorist might say that we read moral principles in human nature, this is only in the sense that it is part of human nature to have reason.
(2) The precepts of natural law are not discovered by 'looking into nature'; they are principles of reason without which we cannot reason about practical matters, applied to the common good of the human race. Not only are they not read "clearly", almost all natural law theorists agree that, except for the very most general principles, they are very hard to think through. Ethics on a natural law account is as difficult as logic or mathematics; the very basics can be recognized fairly easily, but it gets difficult very, very quickly, and navigating it very far requires a lot of serious thinking. Getting to the roots of thinking necessarily involves a lot of thinking.
(3) While natural law theory is teleological, the teleology that matters is the teleology of practical reason, not just any kind of natural teleology. This is why, for instance, New Natural Law Theory, which deliberately avoids anything that even sounds like what is described in the above paragraph, is a genuine form of natural law theory -- while it minimizes teleological-sounding claims, it still regards practical reason itself as teleological, as every sane theory of practical reason does. One can argue -- and traditional natural law theorists sometimes do -- that this NNLT minimalism gives us an inadequate account of common good, but it doesn't affect NNLT's status as a natural law theory.
(4) Not only do natural law theorists not generally draw the conclusion "How nature is reveals how it should be", in the sense in which this would usually be meant, it is inconsistent with every form of natural law theory I have ever come across. Nature may be subject to any number of defects, aberrations, ludi naturae. Natural law theory is not about nature in general; it is only about human nature in a very, very specific and limited way; it is entirely and wholly concerned with what is natural to human reason.
But what is most wrong with the paragraph above is what it does not really mention at all. Any purported account of basic natural law theory that does not begin with a discussion of practical reason is already wrong. Any discussion of natural law theory that does not at any point talk about common good is already wrong. There are two things at the heart of any natural law theory: practical reason and good we share in common as human beings. In a discussion of natural law theory that is supposed to start with the basics, you cannot avoid them, or you have substituted for natural law theory, as the above paragraph does, a completely fictional theory that's not actually natural law theory.
Now, of course, you can get at both of these things in indirect ways -- talk about basic goods, or sustainable and shared rational goals, or about the rational assessment of plans, or what have you. But both practical reason and common good have to be in there somehow.
