Why is the production team making prequels of X-Men rather than sequels?

I think this quote on the X-men: First Class wiki page gives us a decent amount of insight as to why they're making "prequels":

As producer Simon Kinberg read the comic series X-Men: First Class, he suggested studio 20th Century Fox to adapt it. Kinberg, however, did not want to follow the comic too much, as he felt "it was not fresh enough in terms of storytelling", considering them too similar to John Hughes movies, and also that the producers wanted an adaptation that would introduce new characters. Both Kinberg and Shuler Donner said they wanted characters with visuals and powers that had not been seen yet, and that worked well as an ensemble even if they did not work together in the comics.[11] Shuler Donner later said the original idea was to green-light First Class depending on the success of X-Men Origins: Magneto

So we see that they wanted a shift in focus from the main set of characters established in the X-Men trilogy. While quite a few characters were introduced, the main plots revolved around only a hand full of characters.

Another reasoning is that the X-Men universe is quite vast and dynamic. Each character has more than one story arc that just can't be covered in one or two movies. For example, if we look at the story arcs for Wolverine, we get something like this:

• Pre-Memory loss (X-Men Origins: Wolverine)
• Post Memory Loss (X-Men Origins: Wolverine 2)
• Wolverine and the X-Men (X-Men 1-3)

Also, character story arcs criss-cross in the X-Men universe. It is literally a giant bowl of spaghetti, complicated even more by time travel in some instances.

I cannot provide as much insight (or any knowledge about the comics) as DForck42's answer. But from a mere movie viewpoint the finale X-Men tirlogy was a pretty closed end, with many main characters dying, or losing their powers (Xavier, Jean Grey, Magneto).

I guess this can make it a bit harder to start a new story after those events, whereas the time before all those events is still fresh and it might be an easier option to turn there for new X-Men stories (at least for now).

There have been 4 movies since the original trilogy (X-Men Origins: Wolverine, X-Men: First Class, The Wolverine, and X-Men: Days of Future Past).

The reason Fox decided to make prequels instead of sequels is because of the third X-Men movie (The Last Stand).

Firstly, that movie got terrible reviews and a lot of fans hated it, which made Fox scared that a sequel wouldn't succeed. However, the main reason is because The Last Stand really messed up all chances of a sequel by killing so many important characters.

Professor X died, Cyclops died, Jean Grey died, Magneto lost his powers... How would they make a sequel with only Wolverine, Storm, Rogue and Beast?

However, in the latest X-Men movie Wolverine goes back in time and changes the past so that nothing from The Last Stand ever happened, and everyone's still alive. So the next X-Men movie, X-Men: Apocalypse, will be a sequel and not a prequel.