Most universities agree on the deadline of December 15 for graduate application submissions, and on the deadline April 15 for committing to an offer from the university.
My professor claims there is a similar agreement on how early acceptance letters are officially sent out (February 15, perhaps). User @NateEldredge expressed skepticism of this here.
Q: does such an agreement exist?
It's hard to provide evidence that something does not exist, so we ordinarily put the burden on people making claims to provide evidence for them. If your professor makes this claim, can they point to such an agreement? If not, I don't think you should believe them. Not that you need to confront them about it or anything, but if you're sufficiently curious you could say you haven't found anything about it and ask where they heard that. You might also consider whether it actually matters to you at all: would this change your actions in some way? Should it?
The April 15 Resolution setting the earliest date for offers of graduate student funding to expire is well-known and well-documented. I've never heard of anything similar setting an earliest offer date, though in practical terms the April 15th Resolution organizes the application calendar; most applications will be due around December (+/- a month; I agree with Nate Eldredge that there is no such universal Dec 15th deadline), most interviews conducted in Jan-March if they happen, and decisions to offer admission around that same time, often contingent on whenever the group of people on the admissions committee can find an available time to meet. There's not much benefit to offering earlier because the expectation is that students will wait to see what other offers they have before accepting, because that's the whole point of the April 15th resolution: preventing a race against the clock for universities and unfair expiring offers for students.
Not an answer to the question itself, but worth stating nonetheless:
An "agreement" may be an unwritten and unacknowledged one, between just some universities who think that it would be a useful deadline to choose because many others use it as well, not because there is a formal contract between universities. In other words, there is an entire continuum between complete anarchy and having a written, legal, binding contract between all universities in the entire country.
