Yeshivishe kup – Reading Psukim in the Torah even if you don’t understand them is limud Torah and the rule of Talmud Torah kneged kulam applies as far as I know.
However, if it is a Mitzva sheaina yachol leiasos al yidai acheirim (a Mitzvah that no one else can do), you have to do it. I would guess that kibud av v’eim falls in that category.
However, if you are deep in the middle of a sugya and it will disturb your learning, it’s possible that it is different, since it might fall under the category of “chayecha kodmim.” In general, kibud av v’eim is not supposed to be at the expense of your own life, and it makes sense that one would not have to interrupt “real learning” to wash the dishes, especially since it is doubtful that the dishes absolutely have to be washed at that moment and that there is no one else around to do it (just a guess regarding what your Rebbe meant).
I am surprised that your Rav’s wife asked him to do the laundry when he was deep in a sugya. I am guessing that was a rare occurrence, and hence, the reason he only had to decline helping her due to his learning one time in his life.
Based on the way your post is phrased, I am guessing that your Rebbe was trying to be mechanech his students not to try to come up with excuses not to help their parents.