Head to head means 'something', as in, another data point, but it can't supersede everything else. The only way head to head can be the end-all-be-all is if schedules were more uniform and you were going by record, like the NFL. We all know the college schedules are not created equally.
So essentially, the team ranked higher (Michigan) has a better loss (Mich State), and Mich State is ranked lower because they have a worse loss. This has been a consistent theme across college football forever. Remember 1993 when Florida State lost to Notre Dame who lost to Boston College? FSU had the better loss, so they advanced. 2000 - FSU lost to Miami who lost to Washington - FSU advanced.