The obvious counter to this is: Which will give the worse impression: Canceling for a good reason or showing up and being distracted and performing poorly? Companies like the usual FAANG are nice enough to merely give you a 1 year embargo. In other companies I've worked at, you interview for a team and if you do poorly, the team will simply
never interview you again (although you could interview for a different team at the company).
Also: Do you really want to date someone who doesn't care that your cat may have a life threatening problem?
Finally, even if it's not that serious (cat emergency): Do you really want to work/date someone who is that susceptible to this bias? I know it's the norm to fall for first impressions, but for me, it's also a signal of problems I'll have with them in the future.
BTW, my cat had a serious health problem once. She needed lots of immediate care for a few months (at home, away from work). And the vets were telling us that even if she got through it for now, it will come back soon and we should really consider euthanasia - the condition would eventually kill her - not many cats would last a year with it, and chances are her she would be in pain for much of it.
And this all started a few days before I started my new job.
I went straight to my new manager (before my official start date), and explained to him that the cat was my priority - I could take a leave of absence or whatever was needed, but I needed to figure this out (either euthanasia, or time off for treatment options, etc) and could not be anywhere close to 100% at work.
Fortunately he was sympathetic and said I should not worry and do whatever was necessary.
The job turned out to be crappy, and I stayed there longer than I should have entirely because of this.