There is actually no evidence to suggest aspartame is dangerous, it is one of the most researched food stuffs, and all scientific research has shown it is safe for consumption - even for pregnant women. There have been discredited reports into aspartame causing brain tumours and other things, but all have been disproven, often due to a lack of real science use in the initial research and subsequent research being carried out properly have shown otherwise.
But as is often the case, one negative report has a larger longer lasting effect than a hundred positive reports, whether the be on aspartame or vaccinations or whatever. The MMR vaccine doesn’t cause autism, but people still believe it and don’t vaccinate their children as a result.
It brings to mind the phrase “A lie gets halfway around the world before truth puts on its boots.”