A household requires a familial (or otherwise legalized) relationship -- your legal spouse, children/guardians, an elderly parent or in-law living with you, etc. You are living with roommates and none of you have a legal or financial obligation to each other. You can't claim each other as dependents.

If you are not related, not married, and not in an otherwise legal relationship (child/guardian), then you all cannot claim to be in a singular household for tax & benefits purposes.

I mean, this is/was literally a huge reason why gay marriage is/was such a contested political issue. Gay couples couldn't get legally married at one point so they were not eligible for any familial/spousal benefits. As you can see, that's a very big deal just in terms of financials.