But to have the circle you need the same diameter as the height and width the square would be anyway. With a square that had the same height and width, you could have the exact same avatar as a circle. But you can't fit the square in the circle without making it smaller. Seems the wrong way round to me. Your random mix of squares and circles will now be a random mix of inconsistently smaller squares and large circles, surely the worst of all possible combinations if you're hoping for a consistent look.
Personally I would have always supported your choice to have a circular avatar if you wanted to (I think your avatar looks great btw) - it's a shame you, and others, can't support others' choice to have a similarly-proportioned square if that's what they want.
What else is an avatar if not an expression of identity for the user? Confining it in this way limits that expression for some users in a rather arbitrary manner. There may as well be a rule that you are only allowed avatars in a certain colour, or that can only be abstract geometric shapes rather than representational images. I find it to be a backward step.