No one is claiming that a random event (?) occurs the exact same way. They just use statistics, based on some known factors and yes, a lot of guesses.

We know how stars form, how galaxies form, how solar systems form. We know the general consistency of the galaxies around us, and some systems in our same galaxy. It's not a big leap to assume that some percentage of them will be hospitable (for a time) for life, at least life as we know it.

I'd say the arrogant views are that the whole universe was created for us, or that life must be thoroughly plentiful throughout the universe. The least arrogant view is that it's somewhere in-between, but more importantly, to always adapt to the latest evidence.