Message:
Hmm… In fact, “automatic” weight (aka bone heat) uses complex math to compute the weights, and this seems to be intrinsically an unstable/fuzzy process (i.e. if you run the operation several times, you won’t get exactly the same results). This is why the symmetry is not respected by default.

You do can get a nice, symmetric weighting with this method (bone heat), but from the Weight Paint mode. Once parented to armature:
* Select your armature, switch it to Pose mode.
* Select your mesh, switch it to Weight Paint mode.
* Now select all your bones (A), open the Weights menu, and select Assign Automatic From Bones.

Now you will have a symmetric weighting, because the WeightPaint editor by default has its X Mirror option enabled. If you disable it, you’ll see you get again uneven weights…

Think I’ll just add the "X mirror" option to the parent operator, and that will do it ;)