Benjamin Franklin is said to have replied, "What use is a new-born baby?" in response to a skeptic of the utility of some of the first balloon launches.
I suspect that you won't be swayed by the abstract benefits of intelligent life on Earth finding not just proof of life on another body in our solar system but actual life that we could perhaps even launch retrieval missions to return to Earth for analysis so I won't talk about Darwin and his voyages and the theory of evolution that it resulted in as people often do in these conversations.
Instead I'll ask you what you think the dollar value of studying and reverse engineering an alternate or similar biochemical system survives in a world totally different than our own. What sort of applications could this have in materials science? What kind of new materials could we discover from alien life? What kind of novel bio-mimetic applications could we derive from this?
I look around the room I'm in and I see a hardwood floor, I see a differnet species tree making up woodpaneling on the walls. My clothes are made of cotton and rayon, there's some sort of grass woven lampshade above me. books made of paper, paintings with linseed oil paint -- what's the commercial and cultural value of all that stuff to our species?