H1 visa is so-called "dual intention". People holding H1/H4 can choose to either go back "non-immigration visa such as F1, J1, B1/2, etc. or go to immigration process such I140/I485. In most of case, you can apply F1 as long as u/u spouse havn't applied I485. So you don't have to prove that you have no immigration intention unless u already filed I140. If u alreay filed I140, you need talk with an immigration lawyer. If u already filed I485 (in US), u don't need F1 to go to school (when u file F1, u automatically withdraw your I485.)