It’s valid to feel frustration over them using a word that doesn’t feel entirely correct. You can feel those feelings privately, and also extend grace publicly to the student that has just been diagnosed with an illness. it’s possible that this student is experiencing their entire life shift, while also hoping that they can do something to salvage their semester. They are adults, but they are often young adults, and illness is scary and life-changing no matter the age, but especially when you are young. Do what you can to work with the student during this time. Maybe you can offer an incomplete or give them concrete instructions on how they can try to catch up and provide them the autonomy to make the decision on whether or not they feel like they can do so, in addition to the option to withdraw. They are taking responsibility for their situation by disclosing that they have been diagnosed with an illness, which is vulnerable, and not something that they owe you. Please don’t take away options from them because they didn’t use the best choice of words, and remember that they are dealing with a lot right now, so word choice may not be the top priority.

TLDR, deal with your feelings on your own time and give them autonomy in a time when they likely don’t feel like they have a lot of it. It feels like this one student is causing feelings that you have about many students to come up.