Why did people think Paul McCartney was dead?

No, it wasn't their idea. Paul wore sandals the day of the shoot, and it was hot, so he some how thought it would help to take them off for the picture. He says he doesn't know how the rumor was started.
People thought that Paul McCartney had died because on the album cover of abbey road album Paul had his cigarette in a different hand than he usually does I'm not even kidding the whole rumour started because someone noticed it.

The fact is that Paul had his cigarette in that hand so that it could be seen in the photo (marketing reasons).