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I'll break it down further.
We know life is possible, because we're here.
Nobody knows the exact odds of life being created, but we know it's >0. One in a billion? Trillion?
So imagine a trillion sided die. If you roll a 1, life is created.
If you get only one chance, you probably aren't creating life, but if you are allowed to roll the die constantly from the instant of the big bang, until the end of time, you WILL roll a one. Now, imagine an infinite number of planets rolling an infinite number of trillion sided dice for billions of years.
Sure, it's very unlikely for any individual roll to be 1, but it's downright IMPOSSIBLE for NONE of them to EVER roll it.
Don't get me wrong, I'm not claiming that there are aliens flying around and probing people. I don't believe that's true at all. But there is life out there. Maybe it's just plants or bacteria, or some form of living rock that we've never encountered before, but it's out there.
I say it's arrogant because Earth is a tiny insignificant speck in the universe, and assuming that only YOUR planet can randomly produce life is a very self centered point of view.