That is part of the issue. THe 'creationist' says there are problems that there are not. For example, you mention "No transitional fossils". That claim is misinformation, because hundreds of transitional fossils have been discovered When this is explained, and detailed examples given, the information is ignored by the creationist, who repeats their claim, just as if the information was never relayed to them at all.
I have noticed that even when an argument has been shown to be false, that same arguement gets brought up repeatedly. This seems to be a discognitive dissidence where information that does not match preconcieved notions it dismissed.
Many people do not understand what evolution actually is. They keep on asking for 'evidence' about things that evolution does not predict. They keep on attempting to raise the bar on the evidence. Many people who are creationist reject evolution because it doesn't answer 'where the first cell came from'. That question is irrelavent to evolution, because it deals with how life changes through generations.
Before you can demonstrate the accuracy of a theory, you first have to understand what the theory is. A scientific theory is never 'proved'.
What happens is that the scientists uses investigation and tests to try to disprove it. After over 150 years of trying, more and more evidence has come in to substantiate the theory, and no one has shown anyway to falsify it.