My boyfriend lives with me and I pay all expenses. I am claiming him as a dependent and I don't know why I wouldn't be able to claim head of household?
Based on what you provided, it seems you don't meet one test for head of household and it isn't the support test.
1) the dependent must be your qualifying child which your BF isn't or
2) your BF must be a qualifying relative (QR) but for HOH purposes the following type of QR doesn't count
a) a person who is a QR only because he was a member of your household for the entire year
2) is the long way of saying to be a dependent for HOH purposes he must be related to you which he isn't.
Your BF is not related to you, so he cannot be your qualifying dependent for Head of Household filing status. Unless you have a child or some other person you are supporting who is related to you, you file as Single. If your BF has lived with you for ALL of 2023 and had less than $4700 of income (not counting any Social Security) then you may be able to claim him as a dependent, but all you "get" for claiming him is the non-refundable $500 credit for other dependents.
Am I Head of Household?
https://ttlc.intuit.com/questions/1894553-do-i-qualify-for-head-of-household
https://ttlc.intuit.com/questions/2900097-what-is-a-qualifying-person-for-head-of-household
If you qualify as Head of Household, when you enter your marital status (single or married filing separately) into MyInfo, and then enter your qualifying dependent, TurboTax will offer HOH as your filing status.