First, you have the obvious. The coaching change. Along with that comes the fact that tOSU is doing things differently at QB now too. Martell also had to be talked about of transferring before, and may have some ammo related to the things Urban and others may have said to him to get him to stick around that turned out to be lies.
Second, you have the issue with the Urban Meyer scandal. Tate is very close with his sister and can easily build a case that because of his relationship with his sister he has a heightened respect for women and significant disdain for those who abuse women and those who look the other way when women are being abused. As such, he can easily make the case that he is disturbed by the way tOSU handled the situation and can't in good conscience continue to be a student at such an institution, let alone a student-athlete. One might challenge why he didn't transfer sooner, and the answer to that is simple, the scandal broke too close to football season to allow Tate to find another school that would be a good fit for him athletically and academically.