Why do *I* have to find someone to cover me if I'm sick?

I just wondered if this is normal and/or fair. I do understand me being sick is an inconvenience at the end of the day (even if it may be out of my control), but still when I got told that the other day when I said I was sick, I kind of got upset. Again, I know being a manager is hard and being shorthanded is trouble for the company and other colleagues, but If it were me I wouldn't ask someone who is not well to do all that work, or at least I'd try to offer a solution such as "you can work less hours today if you feel up to it" but no. I don't want to seem selfish but it feels a bit wrong. I thought the company had to find cover for you if needed? Oh also, I ended up having to go anyway!

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