This is largely due to the fact that we're wired from birth to look for patterns and find them wherever possible. We pattern seek because way back when, the reward for matching a pattern (say a tiger hidden in the woods) was surviving another day. False positives had little to no consequence; if you run away from danger that isn't there, you're still alive unless you run into the maw of a waiting shark or something.
It can be really hard to talk to someone about their deeper held conspiracy theories. In part, not only do we want to have matched a pattern and seen something hidden; we also want to be part of the few who have Seen the Truth and understood that which separates us from the 'sheeple' who mill contentedly around us. This kind of thinking often self-reinforces, because many theories hold that there's a conspiracy of silence going on which prevents the truth from getting out and it's all up to *us* to make sure that these dark figures don't get away with what they have planned.
Fortunately, a science writer (and totally not a lizard person) has done some math centred around how hard it would be for a conspiracy of silence to exist and remain silent. Since, as he points out in this article, not everyone who believes in conspiracy theory is unreasonable, this might be a good way to engage with people who haven't fallen too far down the rabbit hole and are willing to take a step back and use a neutral tool like mathematics to analyze their beliefs.
This is something that I've believed in for a long time: vast conspiracies fail the smell test because the amount of work required to keep them secret exceeds how much work any group of people could reasonably do. The more people in your vast network of shadowy figures, the more people there are who might talk about it and let things slip. Thinking that someone won't have an attack of conscience or just a moment of loose lips is to fundamentally misunderstand human nature. In movies and television shows we patch this problem by having large panopticons of surveillance that alert stone-hearted assassins and cleaners to possible breaches of confidentiality; but even those would-be counter-measures involve people who are just as subject to the laws of human nature as anyone else. So I'm very glad that someone who actually groks math has sat down and crunched the numbers for us.
And lastly, remember that some conspiracies do exist. They just exist much closer to the surface than we are led to believe by popular media and our own imaginations. Conspiracies leak information proportional to the number of people in them and there's not a darned thing even the most clever plotter can do to completely eliminate that.