Firstly, no idea about the origin of this phrase, but it seems like a poorly constructed idea that is broad enough to generate discussions on any point of view that you want.
What I take from researching is that sharing your troubles shouldn’t be a one way street, if both people support each other it isn’t therapy it’s sharing, which is just semantics at this point. Can I vent about life to my partner or only to my close friends? or do I need to hire a professional?
Alternatively a very direct reading is that your partner doesn’t have the medical expertise to solve your mental issues. Which is very fair, but again lay people can’t be expected to diagnose if their partner is suffering from depression or just sad that their dog died.
A really negative reading of this is just a toxic excuse, “Oh, my boyfriend cried in front of me so I dumped him, I’m not his therapist”
At the end of the day, ignoring this phrase, should I share that I had a bad day with my partner? Should we talk about trauma that we had as kids? Where is the line if there is any?
How about another phrase. No one person can fill every role you need.
The person complaining about dividing relationships and being someone’s other half kinda sounds like they don’t have friends outside of their relationship.
Draw your own conclusions based on your relationship with [insert spouse, friend, acquaintance] and what roles you each want to fill for each other.