Can't I take 1098E student deduction interest as a parent since I co-signed the loan but Turbotax says 1098E has to have my name, not my child's name to take deduction?

You can claim the interest deduction, if you meet the three requirements:

1. You paid the interest
2. You are legally obligated to pay it (co-signing counts)
3.  The student was your dependent, at the time the loan was used to pay for qualified educational expenses (the TT pop up says “when you took out the loan”)

Just ignore what TT is saying.  Treat the 1098-E as if it is yours.