An entire manifesto could be devoted to outlining the case against buying a house with someone else(ESPECIALLY some broad you haven't wifed up/produced offspring with), nonetheless for the sake of brevity:
-NIMBYISM and moronic regulations have made homeownership all but impossible in many sections of The US also
-Maintaining a medium size-large home requires a considerable amount of effort... When you have a highly active career, who the hell wants to spend a large portion of their down time cleaning dead squirrels out of gutters, mowing the front lawn, clashing with the neighborhood association over your latest squeeze sunbathing topless in a backyard that's supposed to be your own, etc etc?
-Most relationships between human beings(romantic and otherwise)generally don't last especially long. Chances are high then that you're going to LOSE a chunk.of change, if you go halfers on a home with a woman. Even if you remain together for a decade, that's still a pretty lousy ROI
-Evidence that the ladies just ain't cut out for 9-5 over a prolonged period of time
https://www.reginalark.com/2022/07/07/the-corporate-workplace-was-never-designed-for-women/ , and that(more importantly)most gals aren't even interested in doing so
https://news.gallup.com/poll/267737/record-high-women-prefer-working-homemaking.aspx is compiling, with each passing day. Thus, the number of women who can really pay this 50% you propose is in the single digits