TurboTax asks questions in the interview  to help you choose the most beneficial filing status that you are qualified for.  If you didn't get the Head of Household filing status, it could be that you didn't meet the qualifications. To file Head of Household you must be unmarried, have a qualifying person, and pay more than half of the cost of keeping up your home. Your filing status is determined in the Personal Info section of TurboTax.

More information about the filing status Head of Household can be found here:

https://ttlc.intuit.com/replies/3288637