Father's Day was not a holiday Astrid had ever celebrated before. Sure, she knew it existed, and yes, she understood the principle of it, but with whom was she going to celebrate it? The father she'd never met? "Yeah, by the by, thanks for donating your sperm so I could exist and then fleeing and remaining anonymous for my entire life." Not the best content for a card, and bloody hard to find. So she and her mother always anti-celebrated by spending the whole weekend in, watching a multi-day movie marathon of films with little to no appearances by fathers, eating popcorn and ice cream and pizza and drinking gallons of soda, tea, and coffee in various forms. They would stay in their jim jams and not bother fixing their hair or putting on makeup, turn off cell phones and computers, not answer the landline but for an emergency, and spend the weekend utterly ignoring the rest of the world.
So it's understandable that when her first Father's Day with an actual father figure rolls around, and there's two of them to do something for, she's a little overwhelmed. John and Sherlock don't expect anything; John knows it's hard to cope with such a sudden and complete change, and Sherlock doesn't actually remember that Father's Day exists.
But that Sunday morning, John wakes up to a cup of tea on his bedside table and an invitation for a "just us" dinner out that night. He smiles a little, thinking of the difference between this shy, honest, withdrawn girl who couldn't even give him her gifts in person and the girl she had been when they first met, full of false bravado and mourning her mother.
Sherlock, on the other hand, doesn't give the date a passing thought until he sits down at his side of the table in the sitting room and sees an envelope with his name written on it. Upon opening, he finds a horrifically generic Father's Day card with a disgusting poem using a simplistic rhyme scheme. Inside, towards the bottom, though, it has possibly the most priceless words he's ever seen written: You know you're quite good at being a detective, but I just thought you should know you're not rubbish at being a father either, so you've got the position as long as you want it.