A tu quoque, or a ‘you too’ statement is generally thought to be fallacious. As with most things thought to be fallacies, this depends on the way it is used.
Now, we can certainly agree that tu quoque considerations have no impact on the truth value of the claim being responded to. So, if a reader of the Daily Mirror newspaper complains that the Daily Mail is biased towards the political right, a response that the Mirror is biased towards the political left in no way refutes it. I take this as obvious and self-evident.
The tu quoque fallacy therefore is the implication that a tu quoque statement does demonstrate that the claim it is a response to is false. Alternatively, a tu quoque could be employed as a way of distracting from an argument in order to avoid having to deal with a point. We might also call this latter informal fallacy* a red herring or “whataboutery”.
What if, however, the response in the above example was not meant to refute the claim that the Mail is biased, but rather to provide some other challenge? If the bias of the Mail is an issue because bias in a newspaper in general is a problem (let’s assume this is what was meant by the initial statement), then one must be against the bias of the Mirror as well. The tu quoque response challenges the Mirror reader to apply their principle universally, and (assuming the tu quoque statement is a true one) must decide between supporting the principle and denouncing the Mirror for the same flaw. Most of the time, it is the principle that is discarded.
There is then some value in the tu quoque response, but we must realise its limits. Even if the Mirror reader retracts the principle because they did not want to apply it to the Mirror, it doesn’t follow that the principle is wrong. For instance, the retraction might have been based on psychological reasons – a recognition of the cognitive dissonance coupled with a strong desire for the Mirror to remain in high regard.
That said, if our goal is to convince someone that their principle does not withstand scrutiny and the tu quoque succeeds as a means of doing so, then so long as we keep in mind that it doesn’t necessarily prove the principle false, we should be satisfied. It can be a useful illustrative tool to have at our disposal, especially when our interlocutor is developing an ad hoc principle to justify a spurious claim.
* I would prefer to call this a “dishonest tactic”, as I don’t really think it qualifies as any sort of reasoning at all.