I honestly don't know. This might be a skill issue on my part (very much not an educator), but I think of it as a language for thinking about structural abstraction, so to me the question is akin to "is there a real-life problem that German relates to?"; I can certainly think of lots of problems that would be made much much easier by understanding the language (e.g., getting around Germany, i.e. noticing abstractions), but it's tough to point to anything for this explicit question other than "conversing with someone in German".

I guess to try and mirror your calculus example, I'd try and motivate why someone should care about abstraction itself, perhaps with examples like 'calculating my taxes each year is exactly the same problem, except the raw numbers have changed'.

Alternatively it might go over better to say something like: "Imagine you have a map with a bunch of points, and paths which you can walk between them. CT is the study of the paths themselves, the impact of walking down them in various routes: for mathematicians, this means looking at things like turning sentences such as 'think of a number, add 4 to it then divide by 2 then add 6 then subtract 1' into 'think of a number and add 7'. Once you've spotted this shortcut on this silly toy map, you'll recognise the same paths and the same shortcut when you see on your tax form 'take your income, add £400 to it, divide by 2, add £600 and subtract £100"