People throw around statistics like they're strong evidence, but they're not. Most times I see someone use a statistical argument online, I shake my head and scroll down to the next post. Here's why.
Statistics have a two-fold trust problem. For one thing, wherever you found the statistic you're planning to use I'd bet it was from a source that agreed with what you're using the statistics to argue for. In that case, how do you know they didn't make it up, given it's in their interests to do so? (And if it wasn't from a source that agreed then they probably just got it from someone else who did.) The only way to get statistics that are reliable to the point that you should change your otherwise well-founded beliefs because of them is to get them directly from someone you trust, and then you most likely run into sample size issues... But suppose you do have reliable statistics. When you present it in an argument why should your opponent believe you? It's in your interests to make it up and statistics are generally not things you can prove to a new person without redoing all the experiments.
Statistics are not nearly as easily interpreted as people think. People often succeed in proving that there is a non-coincidental correlation between A and B and then argue that A must be the cause of B. However, in most cases this ignores the possibility that B is the cause of A, or that a certain C that wasn't considered in the study causes both B and A, or that a combination of A and C is required to cause B. To really draw any valid conclusion from statistics you usually have to see the original study publication so you know exactly how the data was gathered.
It's often hard to make sure your statistic is measuring the right thing. I've seen people argue for gun control saying that America has more gun homicides per year than a bunch of other (smaller) countries who have stricter anti-gun laws... only to find out that sthey were measuring the gun death rate as a flat number rather than a proportion of each country's population. Of course America will have more gun homicides if you measure it that way because America has more people than all those other countries. (Not to mention that argument is atrocious anyway for ignoring the dozens of other factors that could be affecting the gun death rate, such as poverty (more poor people = more people with a higher incentive to commit crimes) and cultural differences, to name a few.) Similarly common fallacies to that conclusion include counting suicides and self-defense deaths of criminals in one country but not in the other, etc.
Who made the judgements? This doesn't apply to all statistics, but for ones concerning things that not everyone can agree on the exact definition of, you run into an even bigger problem than any of the above. Example: a statistic that "70% of sexual harassers are male". Even if you can establish the reliability of the source and the relevance of the figure, you have to ask who decided which cases count as sexual harassment. In all likelihood they had different ideas of what that means than you or your opponent do.