Anton Petrov had a good segment a few months ago that explains why life in the universe may be extremely rare and it isn't mathematically impossible that Earth is the only planet in the whole universe to have life. The common assumption is that because the universe is so unimaginably large, that life must exist elsewhere, but that may not be the case.
The argument revolves around the different possible combinations that exist for amino acid combinations and how the proteins can fold in a way that life can form. The possible combinations are 10^300, while the number of potential worlds in the universe is about 10^30. It seems that for this to occur randomly, it should take longer than the age of the universe to occur just once. This could mean that the fact it happened once here was just an extremely fortuitous circumstance and that we shouldn't expect it again. You also have to consider the physical properties of our planet that allowed this to happen, and that most potential worlds will not have these properties. Also consider that even if it did form elsewhere, it may never have needed to evolve into complex or intelligent life forms, or survive through mass extinction events.
Obviously, there are some assumptions. It is possible that alien life uses a different recipe. We have no reason to believe that the same physical and chemical processes wouldn't apply everywhere though. Assuming anything else is not science as much as science fiction until we learn more.
Anyway, I am sure Anton Petrov explains it better than I can.
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"A pessimist thinks things can't get any worse. An optimist knows they can."
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