Skyrim is a very buggy game, but we love it anyway.
If you are playing on the PC version there are a couple of fixes you can try with the command line.
- To stop Tolfdir from running in and starting the fight prematurely, use TDetect which will stop either Ancano or Tolfdir from attacking each other, allowing the script to progress normally. TDetect can be turned back on again once the Eye of Magnus opens.
On both console and PC the following might have caused the problem, check the fixes that come with each
You may also enter to find a member of the Psijic Order already present in the hall, skipping over the cutscene between Ancano and Tolfdir, preventing Tolfdir from finishing his cutscene. This makes the quest impossible to finish. You must reload a previous save before entering the college to continue
If the Dragonborn encounters a Dragon before entering the college and does not kill it, the cut scene will fail to start, rendering the quest unable to be completed.
If a magic anomaly encountered outside is left alive, upon entering the Hall of Elements, Ancano will speak the beginning lines, but Tolfdir will run into a corner preventing the Dragonborn from being able to fight Ancano. In order to fix this bug, one should go outside and kill the magic anomaly then re-enter the hall, Tolfdir should now run his proper course.
If all else fails you might need to reload a previous save or there is a possibility that the quest is incompletable.