I call this particular fallacy, the "Spartacus Syndrome."
|"I am Spartacus!"|
Have you ever seen the 1960 Kirk Douglas movie Spartacus? At the climatic ending of the film, Douglas, playing the titular hero Spartacus whose army of slaves has just been captured by the Romans, stands up and declares he's Spartacus even though admitting his identity means a hideous death. His followers all rise and, one by one, also claim to be Spartacus, each shouting out "I am Spartacus!." Of course, not all of the slaves were really Spartacus, but one of them, Kirk Douglas, actually was. It would be a logical error to conclude that no one is Spartacus just because they all claim to be. In much the same way, not all religions can be true and not every Christian group can be the one true Church, but it doesn't logically follow no religion is true or that no Christian group is the true Church. Concluding otherwise is just as wrong as concluding that none of the captured slaves was the real Spartacus.
In case you haven't seen the movie, here is the relevant clip:
The existence of contradictory truth claims doesn't mean that all those claims are false, just that some of them are. This can be easily demonstrated by looking at other fields were various truth claims compete. For centuries, there were people who believed the sun went around a still earth and others who believed the earth went around a still sun. While both of these claims can't be true, it doesn't follow that they both must be false. We can conclude that both could be false and that one and that both cannot be true, but it is possible that one is true and the other false. In this case, the Earth orbits the sun, not the other way around.
And this cosmological example shows us how to rationally deal with competing truth claims. We can't simply dismiss them. Just as a long time friend could have picked his way through the throng of slaves and identified the real Spartacus to the Romans in the movie, so too looking at the evidence for the various claimants to be the truth can also lead us to determine which one is really "Spartacus".