CKlaus sat down in silence for multiple reasons at the time. Luna's claims although sudden and out of no where did make him think of a few things. Was it really that obvious that he was no longer human? There was no basis to prove this was true unless someone else knew exactly what he was and the only people that had been able to do so thus far themselves turned out to be just like him.
So in the long run, it couldn't be that his secret was in plain sight. Then again, the argument that the things he did weren't humanlike was still flawed because when he looked at it, there wasn't really much that set him aside from the other kids his age. Back before the war started, if he was seen conjuring up a shadow tsunami, then pretty much everyone would affirm it was some type of wizardry.
