Easy. You are assuming a non-zero probability that life can arise at random, yet you cannot establish that such a non-zero probability actually exists.
IF there was a non-zero probability, it might be simple math, however, since you cannot logically or scientifically establish that such a non-zero probability exists, the math doesn’t actually work in your favor. If you were honest, you would have to assign the probability of life arising at random to a variable of unknown magnitude, but that would not support your biases, so you don’t do that.
tl;dr
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.
The math absolutely works out in my favor. To date thousands of planets have been found around other stars, only a tiny portion we have been able to observe so far. We have found a variety of them with system configurations that mirror ours, with an Earth-sized planet in the star’s habitual zone. Extrapolate that out, and we could be looking at a lot of worlds with at least simple life.
So baring the limits of our equipment to put the issue to rest, your long-winded response is already on shaky ground as we finding that the conditions that led to life arising on Earth isnt all that unlikely to exist for some of these planets if only a few other conditions are met.
But then again, we dont have the equipment, but the likelihood is getting better with each passing year that we could get a signature that some sort of biological process is taking place on these worlds.