My teacher told me that the phrase be necessary to can be used only on people. For example,
Something is necessary to someone.
Assuming she is correct, then this following sentence, the one I want to ask, will be incorrect.
Actually, healthy fats are necessary to our overall well-being.
Which of us is right?
Best Answer
Your teacher is most likely incorrect.
Old Counterexamples
Some high-profile examples, though dated and not a model for modern grammar, counter the idea that be necessary to may only refer to people.
The Second Amendment of the U.S. Constitution (source):
Thomas Paine in Age of Reason (source):
John Locke in A Letter concerning Toleration (source):
New Counterexamples
I did a search of COCA for
necessary to the [N*]
to obtain the following examples. This is not an exhaustive list. Recent examples include Bloomsbury, Freud, and the Vulgar Passions (1990):Intermental Thought in the Novel: The Middlemarch Mind (2005):
"Radical Islam in America" USA Today (2005):
American Heritage (2004):
Meet The Press (Spoken) (2011):
Microsoft–hardly a paragon of the English language–has an error in Windows 7:
Examples of the teacher's claim
A COCA search provides a few hits between 1990 and 2010 (source):
Note: this only looks at "necessary to him"; further searches with her, them, person names, etc. may yield more examples.
Conclusion
In the OP's case it does sound better to replace to with for; however, the sentences above sound fine to me. My intuitive guess is that the phrase be necessary to (excluding to-infinitives, e.g. "it is necessary to kill") is less common than be necessary for, but I lack evidence to back up that claim. Nevertheless, the teacher's claim doesn't seem founded on real-world usage.