Exactly, if Elizier had went out and said what he thought, nothing good would come out of it. The point is to make you think.
One thing i Just wanted to point out, Mr. Hat&Cloak (or, as Hermione calls him, Mr. Extremely Shifty Guy) appears to shape-shift when talking to her. Has anyone considered that he could be a manifestation of Tonks? Thats a bit far fetched, but whoever he is, he either can shape-shift, OR create illusions to make it look like he does.
It's odd. If you think about it, Eliezer's Argument is absolutely correct. But it seems rather unintuitive even though I KNOW it's right. We humans are a bit silly sometimes. On the other hand, we did manage to figure this out, so it's not that bad.