If you’re on a wild-goose chase it means it’s a worthless hunt or chase; a futile pursuit.
Pursuing something that seems pointless or unattainable.
A foolish and hopeless pursuit of something unattainable.
1. I wasted my whole morning on a wild-goose chase looking for my keys.
2. Jonathan came back annoyed after I sent him out on a wild-goose chase.
3. Becoming a movie star can end up turning into a wild-goose chase.
4. Attempting the bar exam for the 10th time may be a wild-goose chase in becoming a lawyer.
bootless errand, fool’s errand, lost cause, merry chase, red herring, snipe hunt, vain attempt, waste of time, wasted effort, wasted labor