My EX (note emphasis on ex) used to do this but to this day I'm convinced it wasn't a clumsy attempt at empathy but rather a ploy to absolve himself of any additional 'responsibility' for the time I felt ill.
A decent person steps up if their partner is feeling ill ... they'll suggest that the poorly one rests, takes it easy, takes a soothing warm bath, goes to bed or whatever's required to ease their symptoms. In the meantime the decent partner would, for the duration, take on as much 'extra' work as they could to facilitate their partner's recovery. Pretty basic stuff like cooking, laundry, cleaning and, of course, childcare.
However, EX would almost always 'level the playing field' by countering any of my health issues with 'equivalent' issues of his own (out of the blue) - meaning that as we were both now 'equally' incapacitated (allegedly) he'd sweve any additional tasks and the absolutely essential stuff like ensuring our kids were safe and fed would continue to fall on both our shoulders. Except it usually fell heavier on mine because once he'd staked his claim so to speak, the amount of theatrical huffing and puffing, sighing and moaning, would play on for ages to ensure there was no sign of his 'improvement' before mine.
Conversely, when he was genuinely ill, I just got on with things to allow him to recover properly. Even then, the amount of 'poor me-ing' would often be disproportionate to the matter in hand - especially when speaking to his mother who'd smother him with sympathy.
There are just some people who are selfish and lazy and who absolutely cannot bear, even temporarily, and for very good reason, not to be the most 'important' person in the household.