Harry and Sherlock took a healthy dislike to each other from the moment they met.
Well.
To be more precise - Harry almost punched Sherlock after he deduced within five minutes of their introduction that she obviously hadn't moved on from Clara and told her that she should stop mixing her drinks so much if she didn't want to end up in hospital again. John had never quite been able to smooth over Harry's ruffled feathers from that incident, and Sherlock maintained that he had just been trying to give her some well-intentioned advice ("If she's in trouble, that'll distract you, John. I need your full focus for our cases!").
John can deal with their antipathy as long as there are no dust-ups in public. But occasionally he does allow himself the unlikely hope that his sister and his flatmate-partner-colleague-friend might some day get along.
Reviews and/or title suggestions for this little chappie are welcome. You may have noticed I'm not very imaginative when it comes to titling these things.