Why are children supposed to take their fathers last name?

I mean it's the woman who has to give birth to the baby and take care of the child and in the modern times, the woman also provides just as much as the man. Then why is it that the woman always has to give up her own name and take the husbands name and also give birth to a kid who's eventually going to take her fathers name. Is it fair?
Why are children supposed to take their fathers last name?
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