Tu Quoque fallacy
Better known as the 'Whataboutery' or 'Appeal to hypocrisy' fallacy, and Latin for "you also", its use is particularly prevalent in political discussions or were the interlocutors represent a 'side' or prescribed position. Essentially it calls into question the moral or intellectual authority of the other side to interrogate your actions or claims because of their inconsistency in acting in accordance with the position they are espousing. It is fallacious because the moral character or previous actions of your opponent are irrelevant to the logic of the argument under discussion.
By using it yourself, it allows you to deflect from criticism by subtly shifting the focus back on to the other person, who now feels the need to defend their side's actions or position before continuing. On the wider stage, watch out for it in politics: 'But whatabout her emails?'; 'But whatabout your party's anti-Semitism/Islamophobia?'; 'But you supported austerity!'; 'But I've heard you say shitty things in the locker room!'.
These issues are not beyond criticism, but by bringing them up when you are being questioned about your failings, it does not answer your own criticisms, only deflects them. If your opponent does this to you the best way to bat it away might be to accept the charge of hypocrisy but return immediately to the question in hand, reminding them that it is still something that needs addressed. Alternatively, appeal to everyone's hypocrisy with something like: "If I smoke 20 fags a day and tell you that you shouldn't smoke because smoking is bad for you, I agree that is hypocritical, but that doesn't make it any less right."