
Kevin C. answered 03/23/19
Theology Geek: Greek, Latin, Proofreading, Writing, ACT-SAT-GRE
I doubt they are being pretentious, though that happens sometimes. Becoming a good writer is challenging, but one of the best ways to improve is to foster a spirit of being "coachable." Beyond college, you are not often going to have the opportunity to receive feedback on your written work, so make the most of it right now. So before I give my answer to your question, I would say that the first thing you ought to do is presume that your professors are correct in their critique of your written word.
It's a great question you ask. Essentially, what you're after is the notion beneath the word.
There is nothing per se wrong with the choice of the word "basically," but in its common usage, it might seem to your professors to be evidence of too informal of a "voice" to your work. Does your writing carry this characteristic? (I'd have to see more of your writings to make a complete judgment.) In other words, your professors are possibly trying to help you avoid too colloquial a tone in your writings. "Basically" is a misused word in our culture. It comes from the Greek word basis (βάσις), which is has to do with stepping, standing, or a foundation. So when you use this word, are you really identifying the very foundation of a concept, or are you "basically" rephrasing your point?
Another possibility is that nonessential adverbs can be a sort of security blanket for a writer. Look at the words criticized by your professors, and ask yourself whether they truly add any meaning beyond emphasis to your work. Yes, "essentially" is more formal in that it gets to the essence (or nature) of the thing. If that's the notion you intend, you might choose that word with better success. But the same problem can occur if "essentially" becomes just another filler word that doesn't add meaning.
Best wishes to you in your work. Let me know if I can help.