Why use extreme value theory? I'm coming from Civil Engineering, in which we use Extreme Value Theory, like GEV distribution to predict the value of certain events, like The biggest wind speed, i.e the value that 98.5% of the wind speed would be lower to. 
My question is that why use such an extreme value distribution? Wouldn't it be easier if we just used the overall distribution and get the value for the 98.5% probability?
 A: If you are only interested in a tail it makes a sense that you focus your data collection and analysis effort on the tail. It should be more efficient to do so. I emphasized the data collection because this aspect is often ignored when presenting an argument for EVT distributions. In fact, it could be infeasible to collect the relevant data to estimate what you call an overall distribution in some fields. I'll explain in more detail below.
If you're looking at 1 in 1000 years flood like in @EngrStudent's example, then to build the normal distribution's body you need a lot data to fill it with observations. Potentially you need every flood that has occurred in past hundreds of years.
Now stop for a second and think of what is exactly a flood? When my backyard is flooded after a heavy rain, is it a flood? Probably not, but where exactly is the line that delineates a flood from an event that is not a flood? This simple question highlights the issue with data collection. How can you make sure that we collect all the data on the body following the same standard for decades or maybe even centuries? It's practically impossible to collect the data on the body of the distribution of floods.
Hence, it's not just a matter of efficiency of analysis, but a matter of feasibility of data collection: whether to model the whole distribution or just a tail? 
Naturally, with tails the data collection is much easier. If we define the high enough threshold for what is a huge flood, then we can have a greater chance that all or almost all such events are probably recorded in some way. It's hard to miss a devastating flood, and if there's any kind of civilization present there'll be some memory saved about the event. Thus it makes a sense to build the analytic tools that focus specifically on the tails given that the data collection is much more robust on extreme events rather than on non-extreme ones in many fields such as a reliability studies.
A: You use extreme value theory to extrapolate from the observed data. Often, the data you have simply isn't big enough to provide you with a sensible estimate of a tail probability. Taking @EngrStudent's example of a 1-in-1000 year event: that corresponds to finding the 99.9% quantile of a distribution. But if you only have 200 years of data, you can only compute empirical quantile estimates up to 99.5%. 
Extreme value theory lets you estimate the 99.9% quantile, by making various assumptions about the shape of your distribution in the tail: that it's smooth, that it decays with a certain pattern, and so on.
You might be thinking that the difference between 99.5% and 99.9% is minor; it's only 0.4% after all. But that's a difference in probability, and when you're in the tail, it can translate into a huge difference in quantiles. Here's an illustration of what it looks like for a gamma distribution, which doesn't have a very long tail as these things go. The blue line corresponds to the 99.5% quantile, and the red line is the 99.9% quantile. While the difference between these is tiny on the vertical axis, the separation on the horizontal axis is substantial. The separation only gets bigger for truly long-tailed distributions; the gamma is actually a fairly innocuous case.
 
A: Usually, the distribution of the underlying data (e.g., Gaussian wind speeds) is for a single sample point. The 98th percentile will tell you that for any randomly selected point there is a 2% chance of the value being bigger than the 98th percentile. 
I'm not a civil engineer, but I'd imagine what you'd want to know is not the likelihood of the wind speed on any given day being above a certain number, but the distribution of the largest possible gust over, say, the course of the year. In that case, if the daily wind gust maximums are, say, exponentially distributed, then what you want is the distribution of the maximum wind gust over 365 days...this is what the extreme value distribution was meant to solve.
A: The use of the quantile makes the further calculation simpler. The civil engineers can substitute the value (wind speed, for instance) into their first-principle formulas and they obtain the behavior of the system for those extreme conditions that correspond to the 98.5% quantile.
The use of the whole distribution could seem to provide more information, but would complicate the calculations. However, it could allow the use of advanced risk-management approaches that would optimally balance the costs related to (i) the construction and (ii) the risk of the failure.
