Well, with ten days of vacation per year, I'd be interesting in any additional time I could take off. But if you have enough (say 25), then I as an employee don't feel that I got the short end of the stick.
It's also a matter of solidarity that those who can support those who can't. In this case, the healthier employees support the ones who are ill.
There's many ways the same support can be given. Why should employees have to support each other in that fashion? There's things like short-term disability that handle absences longer than whatever specific number of normal time off is provided.
According to your logic above, why don't we get 100 sick days per year instead of 10? Some people need that many, fellow employees should support them too, right?
I guess the sick vs vacation day thing becomes a more of a problem in an environment where the rule-followers see a lot rule-breakers taking advantage.
It's also a matter of solidarity that those who can support those who can't. In this case, the healthier employees support the ones who are ill.