The last one died in 1936. They became extinct because of competition for food with the Dingo.
Correction:
The Thylacine only competed with the dingo for food on the mainland of Australia, and even this theory is now being doubted by scientists. The dingo has never reached Tasmania, so was no threat to the Thylacine there.
The Thylacine, also known as the Tasmanian Tiger (though not related to tigers at all) became extinct because the European settlers saw it as a threat to their livestock and petitioned for a bounty to be placed on it. This enabled them to freely hunt the animal, leading directly to its extinction.
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It was humans hunting and killing Thylacines (also known as Tasmanian tigers) which directly led to their extinction. Therefore, had humans never hunted these marsupials, it could be concluded that they would probably not have become extinct.
The authorities should not have reacted to farmers' concerns about the perceived threats to livestock by placing a bounty on Thylacines. The most basic observation of the hunting and feeding habits of these animals would have revealed they posed little threat to livestock.
There are two parts to this: the extinction of the Thylacine on the mainland and its extinction in Tasmania.
The main factor that led to Thylacine becoming extinct in Tasmania was European settlement. Farmers feared this animal was a killer of their stock animals, so they lobbied the government, with the result that a bounty was placed on the Thylacine. They were literally hunted to extinction.
Scientists have also recently proven that, prior to its extinction, the Thylacine had limited genetic diversity. There is every chance that, were Thylacines still in existence today, they would most likely be facing similar problems currently faced by the Tasmanian devil.
Fossil evidence has shown that the Thylacine was once known on the mainland of Australia as well. Theories have abounded on why the Thylacine was not known on the mainland from the time of European arrival. A study from 2012 which compared the size of thylacine fossils on the mainland with those in Tasmania indicates that the mainland Thylacine was much smaller, and was simply "out-muscled" by the dingo after its arrival (the dingo is not truly native to Australia as it did not originate on the continent). The dingo was a bigger, fiercer and more intelligent predator which often hunted in packs, unlike the solitary Thylacine.
Us humans killed them for food and fun . We also took there environment so we could like there instead of them.