From the way Josiah and Rachel's chat went on The Bachelorette, it seemed inevitable that he'd be going home soon, and as it turns out, "soon" meant the very next rose ceremony. Despite the fact that he obviously had a lot of feelings for Rachel, it just wasn't mutual, and one of the best things about Rachel is how hard she tries to avoid stringing people along. But unfortunately, Josiah handled his Bachelorette elimination the wrong way, and his behavior after the ceremony made it pretty clear why he wasn't the right fit.
As soon as Josiah made it outside for his exit interview, he took the opportunity to make all of the men who had received roses look bad. He brought up Adam Jr., the doll Adam brought with him on night one, and he called Alex a member of the KGB because he's from Russia. It just wasn't a good look on him, so it's probably for the best he was sent home.
And it's not just that Rachel didn't feel the same way about Josiah — it also seems like there were other things she didn't like about him, too, judging by one of her tweets during the episode that may be directed at him because she tweeted it during his elimination.
Aside from his behavior after the ceremony, this wasn't exactly a surprising turn of events. During their one-on-one date, Josiah was really intense, and judging by Rachel's expressions during their dinner conversation, it was pretty clear he was coming on too strong. It was too much, too soon, especially for a first date, and even during the date, Rachel admitted that there wasn't much of an attraction there.
But now, Josiah can be set free, instead of competing for the heart of someone who isn't interested, so isn't this really the best possible outcome for him? Somewhere out there, he will find the woman of his dreams, it just wasn't Rachel.