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I was enraged last week to discover that the card that I had bought my dad for fathers' day, at a cost of £3, had the sentiment 'Happy Father's Day' written inside.

Surely, last Sunday was a day for all fathers, and not my particular father? In which case it should be Fathers' day, shouldn't it?

I would be very grateful if you could inform me whether me rage towards these mass card producers is actually justified.

Thank you.
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Don't get mad! Emotion: smile
Father's Day seems to be the correct form.
"father", in singular, has a sort of universal meaning. It's like saying, for example, "the rights of man", where "man" refers to mankind (or perhaps only to men long ago), not to just one man.
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The dictionary I consulted confirms Miriam's answer:

Father's Day n. a day (usu. the third Sunday in June) established for a special tribute to fathers.
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Comments  
I do not agree with you that 'Father' has an universal meaning or that it can be used as a plural. 'Man', indeed, has an universal meaning, and whilst one can say 'Man has evolved over centuries', meaning the collective 'man' (as in mankind), father can't be used in the same way. The only other meaning of 'father' would be in a religious capacity, but once again, in its singular form.
Perhaps I worded my post wrongly? I meant that father has a generic meaning in the expression "Father's Day". In fact, it refers to "fathers" in general, it is not the day of only one father.
I did not mean that the word has an inherent generic or universal meaning that will be present in any context in which it appears.
I apologise if my post was confusing. Emotion: smile
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 taiwandave's reply was promoted to an answer.