There are a few things to consider and clarify:

1. GitHub is not an authoritative academic reference. Journal papers are expected to be thoroughly reviewed and free from most usual mistakes. They have their process for correcting mistakes, which is different from GitHub, where a single person and not necessarily a committee decides what is best for the code. Maybe your advisor does not understand this. In fact, you might quote publications that describe GitHub code, but citing GitHub is pretty much like citing Wikipedia.

2. "Wrong" equations in code might still yield correct results. So it is important to clarify what exactly is the suggested change and impact of the concerned equation and its two versions.

3. Science is not about discussing who is right or wrong on the basis of opinions, is about proving what's wrong and what resists (Popper's) falsification. Try to design tests or experiment which may assert what is right or wrong.

4. Not a breach of academic ethics to participate on GitHub, unless your pull request entailed some intelectual property issue. In some research environments, you are required to waive all the products of your work to whoever is paying you (and that makes perfect sense). So a code fix might be understood to be "intelectual property" which you might not be allowed to waive to the public without someone's authorization.

5. Also, it is not a breach of academic ethics to point out when things are wrong, I'd even say it's an academic obligation. However, how you do this might be a breach of social norms. I'd be very pissed at you if you publicly claimed my research to be wrong without even talking to me first, as doing so is common courtesy. It would be much worse if you were actually wrong, as people who are eager to point other's mistakes often dislike admitting mistakes of their own, let alone making reparations. Of course, if I post a repo on GitHub, I'm expecting people to raise issues on it, and do so publicly. But normally, you talk in private first if you think someone has made a mistake. I think that is how your advisor is framing these events. You might go to him and say "I maybe should have talked with you first". But prefer to do so after completing item 3.

There are a few things to consider and clarify:

1. GitHub is not an authoritative academic reference. Journal papers are expected to be thoroughly reviewed and free from most usual mistakes. They have their process for correcting mistakes, which is different from GitHub, where a single person and not necessarily a committee decides what is best for the code. Maybe your advisor does not understand this. In fact, you might quote publications that describe GitHub code, but citing GitHub is pretty much like citing Wikipedia.

2. "Wrong" equations in code might still yield correct results. So it is important to clarify what exactly is the suggested change and impact of the concerned equation and its two versions. EDIT: From OP's clarification, it sounds like the "wrong" formula was actually an "approximate" expression. Never say an "approximate" equation is wrong, in many fields, accurate formulas and models are either unavailable or really hard to handle, people might discuss a lot on whether a given approximation is reasonable or not, but simply claiming it to be wrong is lacking maturity.

3. Science is not about discussing who is right or wrong on the basis of opinions, is about proving what's wrong and what resists (Popper's) falsification. Try to design tests or experiment which may assert what is right or wrong.

4. Not a breach of academic ethics to participate on GitHub, unless your pull request entailed some intelectual property issue. In some research environments, you are required to waive all the products of your work to whoever is paying you (and that makes perfect sense). So a code fix might be understood to be "intelectual property" which you might not be allowed to waive to the public without someone's authorization.

5. Also, it is not a breach of academic ethics to point out when things are wrong, I'd even say it's an academic obligation. However, how you do this might be a breach of social norms. I'd be very pissed at you if you publicly claimed my research to be wrong without even talking to me first, as doing so is common courtesy. It would be much worse if you were actually wrong, as people who are eager to point other's mistakes often dislike admitting mistakes of their own, let alone making reparations. Of course, if I post a repo on GitHub, I'm expecting people to raise issues on it, and do so publicly. But normally, you talk in private first if you think someone has made a mistake. I think that is how your advisor is framing these events. You might go to him and say "I maybe should have talked with you first". But prefer to do so after completing item 3.