It's not a commonly used word, but if we look at definition 2, here (which you refer to with your comment about appearing patronising), we can see that it's quite insulting.
1.intended for instruction; instructive: didactic poetry.
2.inclined to teach or lecture others too much: a boring, didactic speaker.
3.teaching or intending to teach a moral lesson.
4.didactics, (used with a singular verb) the art or science of teaching.
With all language comprehension, we have to consider the motives of the speaker, ie what were they really trying to communicate? So, if I was a teacher, and one of my students told me that I was didactic, then I could, according to the definition, think "That's fine, she's simply saying that I'm a teacher". However, since we both already know that I'm a teacher, her motivation for saying it with this meaning doesn't make sense - she would just be stating the obvious, it's completely pointless.
So, I would then assume that she didn't mean definition 1, and that she probably meant definition 2: the motivation makes sense here, as she's telling me that I come off as patronising - she's either insulting me or she's trying to help me realise how to be a better teacher. So, I might be insulted, or I might "take it on the chin" and try to not be as patronising in future.
Either way, she risks offense (which is really what your question should be asking: deciding that something is objectively, inherently offensive can be difficult, and is prone to debate. It's more useful to ask if you risk offending people - that's a much easier question to answer.)
EDIT: this answer may appear didactic. Apologies if so.