There are many alcoholic traditions in Russia. And one of them is "the hand that pours the wine can not change". Why is that? I think, even Russians couldn't tell you. Some traditions are so old, that you use them, but don't know the origin of them. If you ask a Russian about it, one can say to you that changing hand can lead to a quarrel between drinking people, others can say to you the alcohol may be changed in its taste, and some people will say to you it is a very funny tradition in drinking culture and they use it only for fun. In short, using this tradition leads to a luck.
Never been presented with that phrase. However, as much as this might upset your sense of equality, I am afraid to say as a male you are expected to pour wine etc. for your wife and all female guests. If you are a slow drinker this may be a little irksome; but necessary nevertheless! Marital bliss vs. Wine Elbow.