"We haven't the same needs" should be correct as well.
It's a more high-flown, articulate way to say it, and it's correct.
We don't have the same requirements should be ok, there's 'requisitos' but its surely a synonym. I'll make like un oso and try necessities next time.
Especially since DL gives the definition of necesidades as "requirements".
Un oso? Ah, now I get it. https://www.youtube.com/watch?v=9ogQ0uge06o
But they really look for a very literal word for word translation...which is not the way a good translator translates!
Necesidades also means requirements!
"We do not need the same things" is not accepted. But it sounds like a perfectly fine translation to me.
Una buena razón para divorciarse