How many time shave you noted that two things are obviously related because one came after the other? For example, my grandfather used to like ot point out that crime increased after teacher-led prayer was taken out of public schools, thus proving that a lack of prayer led to higher crime rates. Mind you at the same time that prayer was taken out of public schools population size increased, income disparities increased, immigration shifted, some crimes (such as sexual assaults) began to be taken more seriously (and thuse more often reported, resulting in a higher official crime rate), and society in general went through a number of shifts. In other words, alot of things happened, many of which actually likley had a causal relationship with crime rates, and prayer in public schools likely had nothing to do with it. However, my grandfather could never be dissuaded from his position.
It's a common logical fallacy called the post-hoc ergo proctor hoc fallacy - the claim that because one thing proceeded (or accompanied) another, it caused the other thing to happen.
The fact is that in any complex system (you know, like life) many things are happening at any time, and it is not difficult to find things that happen at the same time, or coincidentlaly with each other which have little to nothing to do with each other, but if you are inclined to champion or demonize something it's not difficult to claim non-existent associations.
This is where statistics are valuable, and also a problem. There are ways to use mathematics to look at the strength of correlation, and from that make a better assessment of whether or not two events are in fact related. There are many methods, and some methods are relevant to certain types of comparisons but not others. However, when people who wish to push an agenda start doing so, they often intentionally mis-use mathematics in order to create a bad argument, but one that is hard for the layman to penetrate.
I saw a great example of this sort of thing in The Atlantic today. Take a look at the graph:
Now read the short article.
The point? Well, it's not that you can't trust statistics. Contrary to the popular view, statistics themselves do not lie, they're simply statements of probability. People do lie, however, and they may create false statistics to do it.