Why when I try to add Tennessee as an additional state to file a w-2, Tennessee is not an option to choose in the pull-down window

That is because Tennessee does not have a personal income tax.  You should leave the state blank.

There are now 8 states that do not tax their residents’ income: Alaska, Florida, Nevada, South Dakota, Tennessee, Texas, Washington, and Wyoming. If your state is not listed in the W2 box 15 drop down list it doesn’t have an income tax.  Leave W2 boxes 15,16, & 17 BLANK, empty, no spaces.