Do I owe my family an explanation for moving out?

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I'm 21F, currently a 4th-year college student, and my boyfriend is 22M. We've been talking about me moving out of my family's house and staying with him and his family. His mom already knows about it and is okay with me staying with them. I've been welcomed by his family before, so this isn't something completely unexpected on their side.

The problem is that I don't know how, or even if, I should tell my own family.

For some context, I was raised in a broken family, and my relationship with my family has been one of the reasons I've been wanting to leave home. Since the academic year started in June, I've also had to become more financially independent. My father has only given me an allowance twice, around ₱250 each time, and that's obviously not enough to support me since I have 3 days class and I also commute to school. Luckily, I've always been the type to save whatever money is left, so I managed to get by for a while. But my savings are slowly running out, so I started working part-time.

Financially, I don't think moving in with my boyfriend's family would be an immediate problem. He has a permanent job, and I have my part-time job as well. I'm also still planning to continue my studies.

I'm not planning to completely depend on my boyfriend financially either. I want to continue working and contributing as much as I can.

What I'm struggling with is my family.

Part of me feels like I should tell them because they're my family and I'm currently living with them. But another part of me feels like I don't really owe them an explanation for a decision about where I want to live, especially considering the reasons why I've been wanting to leave in the first place.

I'm 21, so I know I'm legally an adult and can make my own decisions. But I still feel guilty about leaving without getting their approval.

So, do I owe my family an explanation before moving out? If I should tell them, how would you approach that conversation?

I'm also open to hearing opinions about moving in with my boyfriend at this age, especially from people who have been in a similar situation.