it sounds like your point is: "some ways of solving problems are superior to others." i've heard this take a million times. one perspective i'll offer to you is, math is not the only way to solve problems. it's not even the best way in many cases. not everything can be solved by defining a narrow goal, and then having a dispute about the methods, and then picking some objective method and then applying it very optimally, or whatever. this is also on you, as an educator, to understand! i could give a bajillion specific examples.
but first, you have to concede: an analogy nobody understands is bad, and you have to own that, and two, it's not really clear, what exactly is your dispute with Design Thinking? it doesn't have anything to do with user interfaces... so why the hell are you talking about it? why "Design Thinking people"? What is your beef here?