When one is asked, is (something) a (something), the first answer should usually be the same: “Why do we care?”
I brought this up once before, in the context of whether (the situation existing between western countries and Islamist terrorists) is a (war). The first response was “why do we care”, and the next one was “we don’t”. You can call it a war if you want, it doesn’t make any difference either way.
Being more precise, the second answer that time, and in many other cases, should not actually be “we don’t care” — we do care a bit, because we want to make sure we use classifications in such a way as we can communicate efficiently. You can call the tail a leg if you want, but it’s a bad idea, because you’ll be misunderstood.
Another question of this type was “Is Pluto a Planet”. The answer doesn’t matter beyond having useful classifications for efficient communication, and there was much discussion last year as to whether the traditional classification of “planet” should be changed for better efficiency.
The Pluto example was used last year by Geoffrey Pullum of Language Log, and contrasted with the question “Is (the relationship between two people of the same sex which has been marked by some kind of public ceremony) a (marriage)”. As ever, the first response is “why do we care?”, but the secondary response, this time, is different. It is “because many public rules and laws, notably concerning taxation, inheritance, and things like that, treat marriages preferentially or differently from other relationships”. That answer leads only to more questions: What are the features of marriages that makes it a good thing to distinguish them from other relationships in these ways, and are those features shared by same-sex couples or not? Therefore, is it a good thing to treat those same-sex relationships as marriages or not?
Pullum was, rightly, criticising those who attempt to sidestep those substantial questions by appeal to dictionary, avoiding the essential “why do we care”, and jumping straight to “The dictionary says no”.
The only time a substantial question can be resolved by finding the answer to “what does this word mean?”, is when an appeal to authority is being used. This is because authorities are expressed in words. But what matters in that situation is not some arbitrary definition of the word in question, but the actual definition intended by the authority itself. The radical green Christian John Papworth argued, some years ago, that his encouragement of shoplifting from supermarkets could not be answered by appeal to “Thou shalt not steal”, because the meaning of “steal”, and of property generally, is not now what it was when that authority was propogated. To be more specific, it did not then encompass the concept of the joint-stock company. His argument was absolutely correct — while there may be (and in my view, are), good reasons for not stealing from supermarkets, appeal to the Ten Commandments is not among them.
Related to an appeal to authority is an appeal to tradition, but for that there is no reason to worry about definitions. There is no reason to say “We give these assorted benefits only to marriages, and traditionally the word ‘marriage’ has been understood to mean only a relationship between a man and a woman”, because one can equally well say, more simply, “We traditionally give these benefits only to partnerships between a man and a woman”, which is equivalent but bypasses the contentious definition. Appeals to tradition carry different weight to different people, but either way they are not changed by bringing in irrelevant questions of definition.
Any other answer to “why do we care” will come down to real questions about the real world, as opposed to the meaning of words. Those are the questions that matter, and they cannot reasonably be dodged by playing word games.