"Why Would Ariel Throw Her Whole Life Away For A Man She Just Met In The Little Mermaid (1989)?"
"Ariel had an entire song about how much she wanted to explore the human world long before she ever laid eyes on Eric. Even after seeing him for the first time and fawning all over him, she never thought about going to see Ursula to get some legs.
The reason she "threw her life away" was because she just watched as her father go into a rage and violently destroy her Human Trinkets collection, something that brought her more joy than anything else. She invested SO MUCH TIME and risked her life to get those things. All that time and effort was destroyed and invalidated by her father in less than a minute.
Sure, Ursula may have framed her whole pitch to Ariel around "you'll get your human man," but Ariel didn't even consider Ursula an option until Triton destroyed her life's work. She no longer felt she could be happy or safe in her father's ocean, so she might as well try to find a life where he can't reach her. Getting a chance to be with Eric was just a nice bonus."