It sounds to me like you're just nitpicking his words. I can't find this quote anywhere, but he's probably saying Wikipedia is taking "stances", to use your word, on subjects where it should instead be trying harder to be neutral and provide multiple perspectives in a balanced manner. Sincerely trying to understand and convey the perspectives of two opposing sides looks vastly different from taking one side, amplifying their talking points, and suppressing or refuting those of the other side.
The counter-arguments to all this all tend to boil down to some form of condescending tone or moralizing:
* left-leaning is just reality-leaning. LoLoLoL right-wingers are sooo stupid!
* Wikipedia should take the left-leaning stance because it is good, moral, noble, and righteous, while the right-leaning stance is vile, evil, unconscionable, and despicable.
If either of those thoughts cross your mind, then, congratulations, you are left-biased. You should try your hand at Wikipedia article editing. I'm sure they'll love you.