I see several reasons why many experts see the shroud as fake. None of those are changed by this recent work suggesting that there is real blood on there, as real blood is readily obtainable and has long been recognized as irrelevant.
I recognize that a lot of people *like* the shroud. That's fine. In fact, if it brings one closer to Jesus, then the "shroud" is great as a work of art. It's also true that if we insist it is real, when the evidence suggests otherwise, then a non-Christian thinks that we fall for hoaxes, and that casts doubt on the gospel itself if they then hear us preaching the gospel. Those two facts (that people like the shroud and that it's not clearly real) are doubtless why the Vatican has been clear that they don't claim it to be real.
From before - The shroud of Turin appears to be a work of art made during the middle ages, and thus only tells us what an Italian artist around 1300 AD thought Jesus might have looked like (or, being that the image looks Italian - maybe this is what the artist wanted Jesus to look like? or just a fanciful image?).
That's clear from many different pieces of evidence. One is that carbon dating of multiple samples at several independent labs all consistently show that the shroud of Turin was made around 1300 AD. None of the excuses to ignore the carbon dating hold up. If they were wrong, they wouldn't have all agreed on the same age around 1300 AD.
The clearest evidence is the image itself, which is shown in this thread and below. The face doesn't match the proportions of a real human being. The forehead is tiny, as if Jesus suffered from microcephaly, and the eyebrow positions similarly don't match how real eyebrows are.
The face is too long - as if Jesus had a stretched out head. Plus, if one drapes a cloth over a face (try it), the sides of the cloth bend down on the sides toward the ears, and one ends up with a widened face image - which is the opposite of what is seen in the shroud painting.
The arms are anatomically too long - as if Jesus was a long armed freak, and even worse, one arm is significantly longer than the other arm! Plus, with a limp human lying on their back, one can't physically leave their hands covering their crotch - they fall to the side (lie on your back and try it yourself).
That hands over the crotch itself shows that this is a work of art for public (not pubic) display. After all, if a dead guy were wrapped in a shroud for burial, why would one bother to put their hands over their crotch - to keep the worms from being offended? But, if this were a work of art by an Italian artist in 1300 AD intended for public display, he probably would put the hands over the crotch. No one would pay to come and see Jesus' crotch, after all!
Look, I'm a hunter. I know quite well that even if one would have used ropes or something to tie Jesus' hands over his crotch for the fun of it before burial to keep them from falling to the side, it's still implausible. That's because bodies become stiff shortly after death, and can't be repositioned. The stiff body of Jesus would have had the arms sticking up & out, and the head down, etc - not laying in a nice peaceful pose. Unless one were making a work of art in the first place, in which case they'd make the art depiction in a nice peaceful pose with a distorted face and arms of different lengths.
Not to mention the fact that this doesn't match the way people are wrapped for burial. For burial, the shroud is wrapped around the person, and no clear image would result. That doesn't work very well for an artist, as the image isn't clear. If, on the other hand, the intent from the start was to make a work of art, one can then imagine a simple folded over sheet as we see in the shroud of Turin.
On top of all that, the artist who made it
confessed to painting it himself. That was mentioned in a 14th century letter to Pope Clement VII by the bishop who investigated the shroud initially.
For 600 Years, Shroud of Turin Has Been Known as a Forgery
There's more, but that's enough to make it obvious that the shroud of Turin is fake. This is a very big topic, of course, and this is only a small overview, but the evidence is pretty clear.
In Christ-
Papias