God's words reiterated that one can change their destinies or at least alter them to a fault.
That's true, but what is believed on generally is that the destinies are unchangeable. In scriptures there might be written something like that nothing can happen against God's will and/or design. It might have a very different exlplanation for it but we surrender like we do not have any power at all.
Honestly speaking, Destiny is a way we use to hide our flaws. For instance, I see this too much in my society. People give (marry) their daughters to someone without really investigating in which circumstances they are putting her into, if the environment of in-laws, the man is apt for her, then they blame the destiny for her discomforts and pains. And, in the names of destiny, these women are taught to manage their lives in whatever situation they are.