“tl;dr”
Yeah, that’s a real scientific argument there...
“An overly pedantic way of saying: Show me an alien right now or else there is no such thing as life outside of Earth, and I refuse to believe that there could ever be such a thing.”
Wrong, I made a simple mathematical argument that you can’t poke a hole in. You don’t want to accept that because it conflicts with your established biases, so you are getting emotional.
“Extrapolate that out, and we could be looking at a lot of worlds with at least simple life.”
ONLY if there is a non-zero probability of life arising at random, which you cannot establish. I’m sorry that you don’t like to confront that fact, but you must if you want your argument to actually be rational. Right now it is not, because you are avoiding dealing with the weakness in your own argument, something an actual scientist would not do.
Well fine.
You can clutch that as if that is the definitive proof of no life outside of Earth, because if you actually read what astronomers are doing and finding (which is based on real observation), you would realize that you are standing on nothing but a string of your self-congratulatory ability and saying that you have mathematically proven that there is no life outside of Earth, and then demanding that I prove your wrong.
Your math isnt any more proof than a guy 120 years ago, who could have used the same statement to say “there are no other galaxies other than our own” or a guy 50 years ago saying “there are no other planets other than the ones in our solar system”.
Mathematical argument < empirical observation
And those observations are showing precisely how narrow and desperate your reliance on that “argument” is.