Why didn't Romeo and Juliet's families like each other?
As the others have noted, there is no reason but it does highlight how silly it was to have it in the first place. If there wasn't a feud, Romeo and Juliet would have lived happily ever after. Then again, this would have been a very boring play without it.
It's never said in the book. All the reader is aware of is that it was a big problem and was continuous to the current situation in the book, until Romeo and Juliet dies.
Overall, why the families were fighting isn't the main point which is why Shakespeare didn't mention it, just like how he skipped a couple details, like Romeo and Juliet having their wedding ceremony.
There was no reason provided in the story to explain the reason why there was an deep and long-standing feud between the Montagues and the Capulets. I think it could have been that they were vying and fighting for power and pride in the social ranking. If there was no feud, Romeo and Juliet would have been blissfully married to each other and all these would not have lead up to this sad tragedy, which both characters died.
It's unclear but it's thought that it's just a fued of power. They're both rich families. It's just a matter of who's richer, who's more powerful. That sort of thing.
There is no obvious reason given in the play. We know it is a long-standing, old, and sometimes bloody feud between two families, and that's about it.
At the end of the play, after the tragic deaths of Romeo and Juliet, the families end the feud.