Say that it finally becomes possible to reach a planet of a nearby star. It's a new technology that enables it, and we can build a spaceship that will support several generations of people during the trip. Maybe it takes 500 years to get there.
Well, 500 years is a long time. It's not as if our technological development will stop in the meantime. In fact, given 100 years of development, we might be able to construct a new ship that will only take 300 years to get to that planet. Which would mean it would overtake the first, and beat it by a hundred years.
In which case, why build the first ship at all?
That's the objection I've heard most recently against building high-speed rail in the united states. For instance, in the context of self-driving cars that might be able to organize themselves into "trains" on the road, or fit conditions where they would qualify for a higher speed limit, etc. While it may be true that we need high-speed rail now, is it going to be as true by the time they would actually get built?