1) History of the Shroud
2) Palynology
3) Weave of cloth
The evidence indicating it is NOT a forgery is the above, plus
1) The degree of anatomical accuracy - beyond what anyone other than a modern could have known
2) The failure to explain the method of production of the image
3) The uncanny close correlation between the wounds on the dead man and the story of Christ's Crucifixion.
I'm NOT a Catholic, but I believe the circumstantial evidence is such that explaining it is NOT what it is purported to be would have to be even more convoluted and unbelievable than simply believing the obvious.
It's funny, but years ago while I was still a protestant I frequently found myself in debates defending Catholic teaching against so-called "Catholics". The ones who claimed to be "devout" or asserted authority from having attended Catholic schools were invariably the worst. Since my conversion I have found that most of these people aren't even Christian let alone Catholic in their beliefs.
Please keep fighting the good fight.