I read it news that:
How did he arrive at this figure? Whats gonna make human race extinct in 1,000 years?
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From what I can gather from a quick Google search, he didn't give a reason. He just said the sentence "We won’t survive another 1,000 years without escaping our fragile planet." in a public lecture and the media picked up on it.
In a previous interview in 2001, Hawking said "I don't think the human race will survive the next thousand years, unless we spread into space. There are too many accidents that can befall life on a single planet. But I'm an optimist. We will reach out to the stars." (source: Wikiquotes) This suggests that his reason for thinking this is in terms of the probabilities of accidents.
I don't have any information about which type of accident Hawking has in mind, but they could include external threats like asteroid impacts or gamma ray bursts, as well as self-generated ones such as war or climate change.
It should be noted that Stephen Hawking is a theoretical physicist, and as far as I know doesn't do any primary research on the possible future of humanity, so he doesn't have any special authority on this subject. It's not an unreasonable thing to say at all, just don't take it as fact just because Hawking said it.