If you qualify for HOH then you are answering something incorrectly in My Info.

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 filing status (single or married filing separately) into Personal Info, and then enter your qualifying dependent, TurboTax will offer HOH as your filing status.

I'm having the same problem. My daughter is younger than 24 and was a student for at least 5 months. TurboTax is forcing me to file as Single and it is not asking me if my daughter is/was a student. I can't change my status to HoH even though I am.

When entering your dependent information be sure to select that the dependent lived with you in the US for more than 7 months. The time away at college counts as time at your home.  So the "whole year" in this case could also be appropriate. 

Additionally, you would need to indicate that the dependent did not provide more than half of his her own support (assuming that is true). 

I did all  that. Three times, in fact. And it tells me my daughter is not an eligible dependent because you aren't asking me whether she was a student for at least 5 months of the year.

When you go through the interview you will come to the question Was (Tour Daughter a full-time student in 2020?).

Here is the criteria for you to be able to answer Yes.

You daughter qualifies as a student if she was enrolled as a full-time student at a school during any 5 months of the year or took a full-time on-farm training course during any 5 months of the year.

The term "school" includes technical, trade, and mechanical schools but does not include on-the-job training courses, correspondence schools or night school.

"Full-time" means the number of courses or hours the school considers to be full-time attendance.

I had to shut down and save, then restart Turbotax to get the student question. Coincidence perhaps, but 5th time was a charm. I can now change my filing status.