I was expecting this sort of comment, but everyone lives in their own world with their own culture and perspective, especially given the large immigrant populations in the West. Yet, the vast majority of people get by not being offended over phrasings that they could take as offensive to their cultural sensibilities if they really wanted to.
I remember being taught a similar thing as a child, about referring to people with disabilities as 'differently abled' instead of 'disabled', and similarly in my home country the government has made an effort to change the word for disability from one which means "improperly able" to "blessed" (poorly translating). But the former has not stuck, and the latter has not changed how poorly disabled people are treated there. Ultimately the changes turned out to be little more than feel-good virtue signaling.
In the same way, what does not using the word 'cure' accomplish in practice? Some word needs to be used in its place, which will take on the same meaning and in a few years people will be getting offended over that too (as any way of putting it will convey the reality that deafness is considered abnormal to the typical human experience). See the progression of terms that are seen as insults to one's mental faculties as a prominent example, even just within the last 20 years of online discourse that I've been around for, we've cycled through variations of retard (tard, reet etc) and are now in the process of doing the same thing with autistic (with the emergence of euphemisms like 'artistic') since the former is now deemed a slur.
Or, using a less provocative example, we don't change our language to be accommodating of religious communities who consider certain things to be insulting to their strongly held values or beliefs. We rightly point out that facts are more important than their feelings, regardless of how many hundreds or thousands of years old their culture and beliefs are.
Edit: If coughs are insensitive, we can instead look at tumors. There are many types in all parts of the body, some are so benign that they can be ignored, others are curable, others are cancerous and still curable, and yet others are so cancerous they are quickly terminal. Additionally, people afflicted with them tend to form a community due to shared experience. But would we stop talking about tumors colloquially as something which needs to be 'cured' because a portion of those in the community don't want to (or can't) get theirs cured?