So, why is it that an infinitely more complicated pattern and structure in biology must have happened by chance?
Actually, what they're looking for is not so much complexity as regularity and patterns. The most complex signal there is is random noise. The heavens are filled with random noise, but no one attributes its complexity to intelligence or design.
Evolution, while claiming to be intellectual and logical, seems very illogical to me.
OK, let's see your logical analysis.
For SETI research, we are looking for an extremely narrowband CW signal. This alone signifies a non-natural origin.