You may be on to something regarding the urge to dance coming from a female, and not the male tutor. Only MR. Stoppard could tell us for sure though.
The truth is, however, that it is essential for the protagonist to be a Thomasina and not a Thomas. The major theme of this play, and indeed the major conflict, comes from the two schools of thought - Enlightenment vs. Romanticism.
Thomasina's opening question "What is carnal embrace?" sets up a romantic/sexual tension between student and teacher. Her relationship with Septimus starts out as an innocent crush of a 14 year old school girl on an older, dare I say, Byronic tutor. It then evolves, three years later, into a budding romance that culminates in a dance and a kiss. Byron is indeed in the air.
This tension drives much of the action. Thomasina's inner struggle between ideas and love is echoed in the differences in the two schools. Her brain wants the Enlightenment, but her heart longs for the Romanticism. In the end the Enlightenment has left her with a discouraging conclusion. Her response, embrace Romance.
This conflict is echoed throughout the play, in both time periods.
This would be quite a different play if these themes were explored by Thomas and Septimus! It would also be different if the roles were reversed, say a Thomas and a Septima - The role of the innocent young girl blossoming into a young woman is a bit more romantic (and less awkward) then a young boy blossoming into a man.