All my points were assuming we meant intelligent life.
Why does the universe being vast increase odds of there being other intelligent lifeforms?
Life and evolution is based on random events.
Without knowing the source of life, we have no way of knowing if it exists outside even our own solar system.
Imagine if life existed on one single asteroid, it crashed into a body near our solar system, and life spread to our little neighborhood.
Why is that scenario any less probable than life existing in random areas of the universe?