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A boy lates for a girl' s birthday party, infact misses it completely
and shows up at the girl's house.
Girl: Kind of missed cocktail hour.
What does the underlined mean?
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Cocktail hour is a period of time before dinner's being served, used for socializing and getting loosened up a little on some beverages. So, if someone has arrived late, he has missed the cocktail hour. I believe the girl is being sarcastic here.
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"Cocktail hour" is a time at which drinks are served to guests at the start of a dinner party or similar. So, someone turning up late would miss it. Here I think it's not necessarily the case that there actually was a formal "cocktail hour" at her party. My guess is that she's being ironic -- saying that he missed the start of the party when actually he missed the whole thing.
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Comments  
"coctail hour" is usually a casual time for drinks and light food before a more formal dinner or party.

I think the first part makes it hard to understand the meaning of the word. Her meaning could be taken one of two ways:

she was being sarcastic...

or

she was trying to say in her own way that he is a little late but she is still glad to see him
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No, she's just being sarcastic because she had an angry face.
Thanks, everyone!