A Flight Instructor departing from a non-towered airport reported that they taxied on to the runway with another aircraft on short final.

Narrative

My student pilot and I completed our runup in the North runup area for a departure on runway XX at ZZZ. We taxied from the runup area to the hold short line for runway XX. I looked to the left for approaching traffic but my visibility was limited by the student pilot and by the left wing of our aircraft. However; I did observe the student pilot look also for arriving traffic and neither of us observed anyone. Neither of us recall hearing another pilot report their position of being on final; but we could have missed it as we were discussing our plans for the departure and the ensuing flight. We made our radio call announcing that we were departing runway XX and as we entered onto the runway; we heard a pilot report 'Going around'. We were both shocked and disappointed that such an event had happened and that we were involved in it. I am beyond thankful that there was no accident and we talked a lot in our post flight briefing about the importance of positioning the aircraft prior to departure in such a way that provides the best view of arriving aircraft and stressed the importance of the sterile cockpit as well as the need to not only look for traffic; but to also actively listen to all radio calls being made.