Surely not everyone wants to kill themselves. Some people probably have things to live for and others don't, but it's impossible to know what everyone thinks about it at a given time when we can't read their minds, so it doesn't make sense to assume that "deep down" everyone just wants to kill themselves.
It probably is the case that everyone at some point in their life considers suicide, whether it's a thought that pops into their head briefly or they think about it for so long that they actually make plans to CTB. Even then, it's hard to know what people actually think about it, unless they open up about it.