Why did most people think that Voldemort was dead even when there was clear evidence that he was still alive?
In the 6th part we learn from Prof. Slughorn that when Lilly died, her magical goldfish also died.
Basically every little piece of magic Voldemort did would have also been gone with him. But they were not gone, like the curse on the DADA-Teacher position.
Why did nobody see this?
Excerpt too large for a comment,
“But what happened to Vol-, sorry — I mean, You-Know-Who?”
“Good question, Harry. Disappeared. Vanished. Same night he tried ter kill you. Makes yeh even more famous. That’s the biggest myst’ry, see…he was gettin’ more an’ more powerful — why’d he go?
“Some say he died. Codswallop, in my opinion. Dunno if he had enough human left in him to die. Some say he’s still out there, bidin’ his time, like, but I don’ believe it. People who was on his side came back ter ours. Some of ‘em came outta kinda trances. Don’ reckon they could’ve done if he was comin’ back.
“Most of us reckon he’s still out there somewhere but lost his powers. Too weak to carry on. ’Cause somethin’ about you finished him, Harry
-Harry Potter and the Philosophers Stone, Chapter-4
Most wizards don't believe that Voldemort is dead.
Actually, the point you bring up may in fact be precisely why people believed that Voldemort was dead. Consider this quote from Chapter Four of Philosopher's Stone:
People who was on his side came back ter ours. Some of 'em came outta kinda trances. Don' reckon they could've done if he was comin' back.
Compare this with Chapter Thirty-Six of Deathly Hallows (my emphasis):
He must speak to the bereaved, clasp their hands, witness their tears, receive their thanks, hear the news now creeping in from every quarter as the morning drew on; that the Imperiused up and down the country had come back to themselves, that Death Eaters were fleeing or else being captured, that the innocent of Azkaban were being released at that very moment, and that Kingsley Shacklebolt had been named temporary Minister of Magic.
In both instances the magic that Voldemort had been using to control people was undone, and that was a sign that he was gone.
In truth, though, not all magic disappears when the wizard responsible for it dies. For instance, the Sorting Hat was enchanted by the Hogwarts founders, yet it is still in use a thousand years later. So the fact that a given bit of magic was still in effect would not necessarily prove that the caster was still alive.
As for your specific example, that may not have been sufficient evidence anyway. As I argued at length here, the existence of the curse on the Defense Against the Dark Arts position is somewhat dubious in the first place, and even if there was a curse it doesn't mean that everyone would know about it. And even if you did know that there was a curse, it would still be hard to use this as evidence. Voldemort disappeared on October 31st. You wouldn't know that the curse was still in effect until almost a year later when a new teacher was needed for the new school year. With no sightings of Voldemort for almost a year, people would likely have already assumed he was dead. And even if they were carefully analyzing the Defense Against the Dark Arts staffing situation, the fact that the current teacher left (or died), wouldn't prove that Voldemort's curse was still operative. That year could have simply been a fluke.
