Of the alternatives mentioned in the question, the 'tough love' idea does not sound particularly plausible to me. If the student's advisor is "much better than him", then the student saying annoyingly good could arise as a result of envy, or from a sense of inferiority, or because of feeling inadequate to meet high standards.
Another alternative is that the advisor is something of a know-it-all, and often is ostentatious about being right.
Or advisor and student might both be excellent for their roles, but with misperceptions occurring on the student's part; or the advisor might be perfectly ordinary, and the student lazy; or any of a number of other cases might apply, which the given information does not disambiguate.
There is no sense of rudeness in the phrase annoyingly good, but as described it's ambiguous and unclear and it seems unlikely anyone would benefit if the phrase were to appear in a webpage.