50% of the time there will be an even number of geese, forcing one side to be longer. Everyone has already noted that.
When there are an odd number of geese lining up randomly, they will be longer on one side 2/3's of the time, given the overly simplified three options:
1) longer on the left
2) longer on the right
3) evenly matched
So, in combined odd/even cases the best it can ever be is 17% of the time the two sides of the V will be balanced.
Now take it a bit further...
The probability of balanced V legs goes way, way down once you start considering the permutations of 1/2/3/4/etc. birds on each side, since for any
n geese there will be
n-1 unbalanced flight patterns, but only
1 balanced flight pattern.
For example, if you consider 9 birds, there are 8 possibilities of an uneven distribution of geese along the legs, and only 1 that produces balanced legs of the V, so given a random distribution, that's 89% of the 9-bird gaggles that will be uneven. The odds, of course, decrease even more as you add more birds (19 birds has a 95% chance of being an unbalanced V), since in only one permutation do they come out balanced. Odds grow better with fewer birds, but the very best you can get is 1/3 of the 3 bird case will have even V legs.
Taking the 9-bird case as an arbitrary median number of birds, add in the 50% of the time when there's going to be an even number of birds, that cannot be balanced, and that gives us ~94% of the time the V legs will not be even.
I suspect ultimately that it's just because geese cannot count, geese have no foolish desire for geometrical consistency, and they all like to fly next to the popular one...
However, maybe it's because competition badminton shuttlecocks are only made from the left wing feathers of geese, and the geese thereafter list to one side.