Por que o marido de Louise a deixou?

O marido a deixou porque descobriu que ela sabia da morte das filhas, mas não fez nada para tentar evitá-la.

HANNAH
Are you gonna leave me like Daddy did?

Louise snaps back to full attention on her daughter.

LOUISE
Hannah, honey, your father didn't leave you. You'll spend time with him this weekend.

HANNAH
He doesn't look at me the same way anymore.

[...]

LOUISE
I'm... That was my fault. I told him something he wasn't ready to hear.
[...]
Believe it or not, I know something that's going to happen. I can't explain how I know, I just do. When I shared it with daddy, he got real mad. Said I made the wrong choice.
[...]
It has to do with a real rare disease...

Louise então retorna ao presente e conta a Ian sua realização.

LOUISE
I remembered something
[...]
Why my husband left me.

[...]

Louise wipes her eyes and struggles to find her game face.

Infelizmente, a novela fonte, História da sua vida, não aborda por que Ian e Louise acabaram se separando, sugerindo que era apenas uma invenção para o filme.

As outras perguntas tocam no diálogo, mas a resposta, aqui, é realmente o cerne do próprio filme. Eu adicionei spoilers, já que não há como falar sobre isso de outra forma

Louise is experiencing time in reverse. That's the gift of Abbott and his kind. Once you understand the language, you can "think outside of time". That's how Louise knows what to say to the Chinese general and stop the pointless fight that was coming.

Quanto à questão

Louise's daughter has a rare and incurable disease. We know this because her daughter dies. But it's an incredible burden to bear to know what sorrow is to come, and yet to choose it anyways. But at some point she tells Ian she knows their daughter will die. But how would you feel to know that someone made a choice, involving you, that would one day lead to your heart being broken? For Ian, the answer is he felt anger. Anger that she went ahead in having a child she knew would die.

Seu marido ainda não a deixou, mas ele vai.

She had visions of her future self with her daughter being treated for cancer. In future, her husband, Ian leaves her when he comes to know about their daughter's illness. She knows this in present time already, and still chooses Ian as her life partner.

"If you could see your whole life laid out in front of you, would you change things?"

Ele saiu porque não concordou em trazer a filha para o mundo, sabendo que ela morreria de câncer em uma idade tão jovem. Suponho que Hannah sentiu a diferença porque seu pai não podia olhá-la sem sentir seu coração partir sabendo que a perderiam tão cedo. A personagem de Amy Adams, no entanto, escolheu conhecer sua filha e experimentar o tempo que eles tinham juntos, apesar de saber para onde essa jornada levaria. O tempo que eles tinham valia a pena, a dor e a perda. É um filme lindo.