The head of household does show as an option for me

You must be eligible for Head of Household before it will be offered as a Filing Status.

When completing the My Info section of the program you must enter a qualifying person as a dependent before you are asked any question to confirm that you are eligible for that status.

See this TurboTax support FAQ for Head of Household - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-filing-status/qualify-head-household-2021/L0NxUtVc2_US_en_US?uid=lnkgoi8u

And this support FAQ if you are married for Head of Household - https://ttlc.intuit.com/turbotax-support/en-us/help-article/taxation/married-person-claim-head-household-filing-status/L078u1RSW_US_en_US?uid=lnkgplrs

Head of household is a filing status, not a marital status. TurboTax does not ask you to select your filing status. It asks for your marital status and other information, then it recommends the best filing status for you. TurboTax will offer head of household filing status to you if you are eligible for it based on the marital status and other information that you enter.

@jas2dajas-yahoo- in IRS jargon, you are either UNMARRIED or MARRIED.   Those are the only two categories. 

If you are UNMARRIED  and other people live in your household, you MAY be able to file HOH. 

if you are MARRIED, but lived apart from your spouse for the last 6 months of the year, the IRS deems you as 'considered unmarried'.   Under this circumstance, if your child lives with you (along with other requirements), you MAY be able to file HOH.

Simply being the 'bread winner' in your household doesn't make your filing status HOH in the eyes of the IRS. 

this is a GREAT schematic that explains how it works - see PDF page 50.

https://www.irs.gov/pub/irs-pdf/p4012.pdf