Michael Sicinski’s review published on Letterboxd :
This is a difficult film to evaluate, in the sense that it is hyper-focused on a single topic because that topic (fertility / childbearing / potential parenthood) has become the near-exclusive focus of the couple who are the film's subject. This can make Private Life claustrophobic and a bit exhausting, but this is entirely by design.
It's a film about being so consumed with a problem that you just want to find a solution and never have to think about it ever again, but at the same time being so consumed for so long that you're losing sight of what your life looked like without it as the structuring principle.
Private Life is a film of used-to-bes. Rachel (Kathryn Hahn) appears to still be a writer, but she is sidetracked by the fertility quest. Richard (Paul Giamatti) was once an experimental theatre producer of some note, but it appears, as the LCD Soundsystem would have it, that he has lost his edge.
Yes, the heart of the film is ostensibly the familial conflict that results by having their (non-biological) niece Sadie (Kayli Carter) volunteer to be Rachel's egg donor. But more than this, it's about failed compromise. Artists are supposed to leave a legacy. If you can't do that, you can at least have children (and then use them as an excuse -- "I could have gone further, but I chose to raise a family instead").
But what if you find you can do neither?