Struggling to look at grammatical modifiers

I have a passion for English, and I am trying to improve my fluency day by day. Today, I am quite confused when my teacher, a non-native speaker of English, tells me that a sentence in my essay is grammatically wrong and does not make sense.

Here it is:

"It is believed that only excellent academic students should attend the university, (which is) to the extent that I beg to differ."

And is "which is" obliged to be there? Can someone help me to get the picture?
I am hoping for any contribution from you guys. Thank you.