They couldn't stand up to the environmental pressures so they lost to natural selection. Even if they were hunted to extinction, humans are a selection mechanism. It's how things work. And we have selection mechanisms operating on us (namely ourselves), so one day we might be extinct and it will also be a result of selection.
If there wasn't a reason for animals to be going extinct, how could they go extinct in the first place?
Either this is a really dumb question or it needs some rephrasing.
The principle of causality states that for any event to happen, it requires a cause, in this case the event being animals going extinct.
So obviously yes, animals going extinct happens for a reason.
The main reasons why (in a basic approach) are: If an animal is hunted by predators faster than it can reproduce it will die off. If a human interferes with the food chain by using chemicals such as DDT this can kill off entire species at the top of a food chain. If there is a climate change (such as +2 degrees due to global warming) animals will suffer to adapt and may die due to this change. But, there are many many more reasons why animals may become extinct and they are far more complex than what I have covered here.
To keep their populations stable, individuals of a species need to acquire enough energy to mature, and have enough offspring survive to maturity to replace the parents.
Unfavourable conditions can impinge on these needs. Predation, limited food supplies, competition, disease, unfavourable climates or other environmental factors can mean fewer individuals survive to maturity.
If the species can find a place where conditions are favourable, a small population might survive there until conditions improve. Or if a species can adapt fast enough to the new conditions, it might evolve to survive.
But if adverse conditions are bad enough, last long enough, and the species can't find a favourable place or adapt fast enough to cope, then the population can fall below a critical concentration for healthy reproduction -- the so-called 'gene pool' (sometimes a few thousand or tens of thousand members in the same place.) At that point, the species is doomed to grow weaker and eventually die out.
The extinction of one species might make space for another, but sometimes one species dying out can put pressure on other species too, since species depend on each other to survive.
People often talk about evolution as 'survival of the fittest', but that's not true. It has been estimated that some 98% of all species which ever existed on earth are now extinct -- no matter how fast, strong or hardy they were. Some have been pressed to extinction by human activity, but others have been killed off by the environment itself.
So there's not one reason for all extinctions, and often it's more than one reason causing any extinction. You could think of a fire forcing someone to back up to the edge of a cliff, until there's nowhere else to go.
I hope that may help.