Science and Engineering do not use opinions, they use facts, derived from first principles. In comparison, the entire legal system is a clown circus that would be a comedy if it's results weren't so tragic.
In the very first paragraph of his 1881 book titled The Common Law, Oliver Wendell Holmes, Jr. expressed similar thoughts in a somewhat different way:
"The object of this book is to present a general view of the Common Law. To accomplish the task, other tools are needed besides logic. It is something to show that the consistency of a system requires a particular result, but it is not all. The life of the law has not been logic: it has been experience. The felt necessities of the time, the prevalent moral and political theories, intuitions of public policy, avowed or unconscious, even the prejudices which judges share with their fellow-men, have had a good deal more to do than the syllogism in determining the rules by which men should be governed. The law embodies the story of a nation's development through many centuries, and it cannot be dealt with as if it contained only the axioms and corollaries of a book of mathematics. In order to know what it is, we must know what it has been, and what it tends to become. We must alternately consult history and existing theories of legislation. But the most difficult labor will be to understand the combination of the two into new products at every stage. The substance of the law at any given time pretty nearly corresponds, so far as it goes, with what is then understood to be convenient; but its form and machinery, and the degree to which it is able to work out desired results, depend very much upon its past."
So, you're in solid company when you point out that exacting principles of logic have never played more than a limited (albeit very important) role in the course of our legal development.
My primary issue with legal methodology is that it relies too heavily on prior opinion, and not nearly heavily enough on deriving a result from fundamental principals.
It operates much like a compound equation in which subsequent iterations will yield results which are increasingly wrong. Errors are expanded over time, rather than resolved.
This is how we got "Anchor Babies"; A nonsensical creation by the judiciary which has simply allowed the compound errors to pile up to the point of absurdity.
Modern legal method often relies so heavily on a string of prior precedent that it becomes a rickety creation which cannot withstand the slightest jostle.
As I have said before, "If Architects built buildings the way Judges administer law, the first woodpecker which came along would destroy civilization."