Citabria pilot reported a runway excursion during a training flight after a balked landing with an instructor when confusion and communication issues resulted in opposite control inputs by the student and instructor; resulting in descending back to the runway surface and the aircraft stopping in the grass.

Narrative

During training for a tailwheel endorsement; I began a go-around due to a balked landing. The aircraft landed and veered off the runway. There was no damage to the aircraft and no injuries.Weather was clear and wind was calm. Cleared for the option and following a perfect approach and gentle touchdown; the airplane kissed the runway and then inexplicably started ascending. This was not a bounce. I made the determination that we were too high to salvage the landing and quickly initiated a go-around after checking the airspeed of 65 MPH; which is more than enough to fly the airplane out of ground effect. I did not say anything to the instructor as there was little time. Suddenly; after the airplane was ascending under idle power; it began descending under full throttle. I instinctively pushed the nose down to gather more speed. After this point; the exact timing of events is a bit cloudy as things happened quickly. But around this time I realized the instructor; who was behind me; was operating the aircraft controls and to some extent we were struggling against each other. The instructor never said a word. He never said 'my airplane'. We touched down again and veered right off the runway then came to a stop in the dirt and grass beside the runway.I discussed this with the instructor trying to understand what went wrong. I had expected this to be my best tailwheel landing. We discussed that the approach angle; airspeed; attitude was perfect on a clear day with calm wind. We discussed that the flare and power reduction to idle was done correctly and at the right altitude; and that upon a very gentle three point touchdown that I had correctly pulled the stick full aft. My question to the instructor was; how could this happen? Why did the aircraft start to ascend with idle power and no bounce? Why did it descend with full throttle when we were at an airspeed fast enough to lift off and climb out of ground effect and the nose pointed down to increase airspeed? His answer was something to the effect of; these things just happen sometimes. He asked me what I thought happened and I simply could not understand what went wrong. We discussed that he was taking aircraft controls which were sometimes counter to the control inputs I was attempting. We discussed that he never said; 'my airplane' and that he never said anything at all until we were stopped. He said he did not have time to say anything because he was busy trying to get us safely on the ground. He said he chopped power only after we were off the runway.It was not until later that I remembered he previously told me that he was going to mess around with one of landings for training purposes in order to train for the event of recovering a landing that wasn't going well when there was no option to go around due to weather; mechanical or other circumstances. At the time he told me he was going to do that on one of my landings; I did not think that much of it. I can not prove he intentionally meddled with my landing. However; if there was a landing for him to do this; this particular one would have been the best time to do it for several reasons. This was my last day of training. It was on a three-point landing; which likely would have been my last one training with him; and a landing technique that I had become competent enough completing. Weather was no factor. He would have been unlikely to do anything to my wheel landings as I was not competent in wheel landings. And; of course; he told me he was going to do this. He had zero communication with me while the go-around was going awry. While this is somewhat speculative; I feel it is necessary to include this information as he told me he would do it; and he did not communicate at all while we both struggled against each other on the airplane controls. This; of course; was my worst landing in this airplane (or ever for that matter). In every other landing that did not go quite right; he explained that the the flare was toohigh or low; speed was off; attitude was not right; etc. However; for this landing the only explanation was; these things just happen sometimes.