Well... not just that.
We (and I do mean I as a part of we) are looking for evidence that there may be *intelligent* life in other solar systems.
Our definition of intelligence is, fortunately, much easier to match than many others'
"Intelligence is shown by the operation of large antennas"
Ideally, of cource, they are emitting (so we don't have to wait), and have something to say (unlike the satellite television broadcasts sent out from Earth).
So we are trying to find out how common life is elsewhere (other planets to start with: they are closer and so easier to investigate than other stars!), to get an idea of how far too search is far enough.
In the course of our work, we are developping new and improved data processing techniques, telescope concepts, and a lot more (and we have the - useable - patents to show it).
True, we have not found anything so far - besides being able to do better detection work than NASA for specific topics. So there is a component of belief, that something is out there to be found, which may seem off.
But given the resources we've got, the size of the universe, and the time scales necessary, the amount of study we have performed is tiny. For SETI, messages can literally take centuries to be received, and someone needs to pay attention all that time.
So perhaps the assumption that there is life elsewhere is too optimistic (though the sheer number of stars goes against this), but we are aware of the fact that our work probably will not produce results for a *long* time. But if it isn't done, nothing ever will come of it.
And if we get the money (and Moore's law does not break down too badly we should be able to get decent coverage of a significant portion of the galaxy within 60 years or so. If by then nothing turns up (and we have actually done the job), we will at the very least acknowledge that life is a lot less common than we hoped.
And if we have the resources to do it, we'll change our search methods, not by looking for UFOs, but thinking about what and how to establish beacons that can outlive us, to tell future worlds about all we have acheived (or other things).