Here’s the classic moral story version people usually mean:
The Crow Imitating the Pigeon’s Walk
A crow once saw a pigeon walking gracefully near some houses and being fed by people. The crow thought the pigeon’s life was easy and happy. Wanting the same comfort, the crow began to imitate the pigeon’s walk.
Day after day, the crow practiced walking like the pigeon. But it could not do it properly. Worse, it slowly forgot its own way of walking. When the crow finally tried to return to its old life, it couldn’t walk like a crow anymore—nor like a pigeon.
Ashamed and helpless, the crow realized its mistake.
Moral
Do not imitate others blindly; be yourself.
(Also said as: Trying to copy others makes you lose your own identity.)