I don't know that people are avoiding the use of calculus where it's appropriate. Rather, they believe that they will never encounter a situation where calculus is the appropriate tool and thus claim that they don't need to learn it.

It's a shame, because understanding differentiation and integration has had a tremendous impact on the way I think. It literally was a gamechanger for me, and it's worth it even though I only use it in thought exercises now.

They guessed at the answer (these are people doing mechanical and electronic designs). They'd test the design, and it would not work. They'd guess again, test, did not work. Quite a bit of time and money would be wasted, whereas some calculus would give them values for their components that would work the first time.

I've also seen people look up formulas in a book, and misapply them with no understanding. The formulas are understandable if you know calculus, but these people would get answers that didn't work and would just be befuddled.

I was one of those types who had a lot of problems with math in primary school because the style of "here are 150 problems for your homework tonight, just like every other night" didn't work with my learning style at all. It took me a long time to overcome this, and while I can't really give an example of this with calculus, I've run into this with other similarly "advanced" mathematical branches such as combinatorics, which comes up in all sorts of CS contexts dealing with trees or similar data structures.