Believers in the Shroud will have a plethora of arguments to appeal to- although I personally find only three of them persuasive. The first one is that the Turin shroud is unlike anything we've ever seen. They will point out the disturbing fact that nobody has ever replicated it in perfect detail. This argument is only half true though- scientists have created similar replicates using primitive medieval tools- but nothing that is EXACTLY the same. It's an argument from silence, but I guess that's better than nothing.
The second argument is that is that the image on the shroud of Turin must have come from a corpse; although once again other scientists deny this (see this article). The third argument is that, in conjunction with the second argument, the figure on the shroud has very similar injuries to the historical Jesus- so it couldn't have belonged to anyone else. For example, it has head injuries that look like they were caused by a crown of thorns. The body also appears to have remained under the sheet for very little time, as the shroud contains no traces of decay. Also, they will point out that if the shroud were removed from the body in a conventional manner, the blood stains would have looked slightly different. For more information of these arguments, check out Gary Habermas' article here.
Well- there are many ways a Skeptic can retain their skepticism even if they do accept the validity of the above arguments. For starters, some shroud scientists believe that there are theories as to how the image could have gotten into the shroud in a purely naturalistic way. For more information, I would recommend these articles from Raymond Rogers, a popular, pro-authentic scholar of the Shroud of Turin here, here and here. Secondly, if the shroud's image is proven to be from a corpse, I can only guess at why the figure seems to resemble the biblical depiction of Jesus. Perhaps it is from Jesus after all (although the image got there in a naturalistic way). perhaps the shroud was stolen off another corpse, that suffered a similar fate to Jesus. Other shroud supporters have pointed this out (see the bottom of the page here). Or perhaps, as many have suggested, the whole thing is a hoax, and we've wasted our time. I don't have a clue as to how a naturalist can prove the Shroud of Turin is inauthentic; but then again, most shroud advocates admit that they likewise cannot prove that it is authentic. As Dan Porter, owner of a pro-authenticity website states (in this article):
"About 100 scientists, archaeologists and historians representing a broad spectrum of Catholics, Anglicans (Episcopalians), Protestants, Evangelical Christians and non-Christians attended the conference. Most are academics. Many are retired and have time to devote to many hours to the study of the shroud. Almost all believe at some level that the shroud is genuine, even if they cannot prove it."So I suppose all we can do now is sit back and watch the Skeptics and Believers duke it out, as they always do