Okay, I've said a bunch that I don't headcannon Caleb leaving on purpose.
Buuuut, I can definitely see that there is a chance he could have left Belos on purpose.
Here's what might have been the reason:
First off, back then, children were an "out of sight out of mind" kinda thing. They were objects to not get attached to because of the high chance of death. So Gravesfield most likely hated the brothers. Philip especially, because not only was he the youngest, but he's canonically schizophrenic. So, there is a chance peer pressure came into play because Caleb was an artist in woodworking (which was a job that PAID) which also could explain why Belos keeps trying to one up Caleb with his dynamic with Hunter and the Grimwalkers. (But it's also cannon that Gravesfield favored Caleb more)
Next is the fact that both brothers have terrible communication. Caleb never told Philip that he didn't want to be a witch hunter (because Caleb is stuck in his own head), and Philip never talked to Caleb about his dislike of Evelyn until his hate boiled so bad he acted. Caleb must have thought that he wasn't needed and left without a word.
Going off of that, back in the 1600s, you would only live to be in your 20s or 30s, especially in America during that time. And Caleb never had a parental figure to rely on, so he couldn't comprehend the fact that Philip would still needed him despite being a teen. Caleb became an adult at a young age, so he could have thought Philip could too.
Evelyn's influence could also have a part to play (as Caleb is seen caveing into peer pressure all the time) especially when he did go to the boiling iles and saw that things were much calmer there that also could have played into it as well.
Not only that, but Caleb was definitely in a survival mode a majority of the time due to the fact that hundreds die just in the winter the rest of illness and starvation. So, seeing a place without that might have convinced him.
But religious pressure might have pushed him into silence until he left.
I honestly rarely see this done well, so I thought I would share my view on it