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The "Law School changes how you think" line seems to be a popular one, but I'm not sure I buy the premise that it's inherently different.I've done both.
Law teaches how to bring rigour to fuzziness. In software we can set boundaries and push the fuzziness back into the problem domain. Lawyers can't do that, they must address the world as it is.
Let me explain what I mean.
Suppose you use constants with values for HOT, WARM, COOL and COLD. In a normal computing system you will need to define these precisely -- you'll need to give float or decimal values to the thresholds between them.
By setting those thresholds, we simply make the complexity go away. Users wind up carrying the bag for any paradoxes that arise.
Lawyers can't do that, they deal with linguistic variables:
The reasonable person similarly circumstanced.
The buyer at arm's length without notice.
Offer and acceptance.
Reasonably foreseeable.
You can't give any of these a hard value (though the general features of each are pretty clear for almost all cases). They are fuzzy sets.
Dealing with fuzzy sets without destructively reducing it to ordinary logic is almost unique to law. About the only other people doing it are some control engineers and the attendant theoreticians.
edit:
I'd also add that the experience of extremely careful examination of facts and teasing out subtle distinctions are useful skills. So too the learned ability to do that with buckets of documents, quickly, and then having to draft reasonably straightforward briefs or case notes.
I find that skill particularly useful when discussing requirements / user stories.