A leopard has absolutely no choice in how its spots are displayed. None at all. It is born with them and has to deal with them whether it likes them or not. Even if the leopard wanted to change its spots, it can't. Even if you wanted to change the leopards spots, you can't. It's beyond control.
When you apply this saying to a person who has made a mistake, be it the first time or a repeated mistake, you've basically shot them dead. You've just told them that this is as good as they'll ever be - They will never grow, never learn from their mistakes, and they will never change to be a good person. Any hope they had in themselves to become a better person has been crushed by your horrible words.
The difference between a leopard's spots and a person who makes a mistake is choice. A leopard has no choice in its spots, but a person has a choice to change. People can become better, they can learn and not make the same mistakes, but only if they know they have that choice. If all you ever tell them is that they'll never learn and that they'll always fuck up, they're going to believe you. Especially if you're a person who is supposed to love and support them. How soul crushing.
I hate that saying. Hate it. Hate it. Hate it. Human Beings will always have the ability to change. Always. Whether they choose to or not is a completely different story, but you're in no position to tell them they can't. How the fuck is anyone suppose to become a better person if you tell them that this, the fucked up person they currently are, is all they'll ever be ?