Or more accurately, you cannot avoid paying for it (as it is collected in employment taxes). The employer has to pay 4,35 % as sjukförsäkringsavgift, as well as other payroll taxes that total 31,42 % of nominal salary (2017).

https://sv.wikipedia.org/wiki/Arbetsgivaravgifter_i_Sverige

Is that in addition to income tax?

Yes but that's "paid by the employer" which means that it's on top of nominal salary, but obviously included in the total tax burden.

Employer pays $6000 per month, nominal salary is $4565, and employee's income tax 35 % => employee gets $3000.

Of course, it was merely an example of an unhealthy obsession I've personally seen. There are many more. Another would be neglecting to save anything for retirement because you believe your home is your retirement fund.