Why did the Tessier-Ashpool family create two separate AIs with an assigned mission to find each other?
I never understood the actual practical reason for that so it just felt like a MacGuffin, an arbitrary goal to drive the plot.
Why not create them as one AI in the first place, and regardless of whether they're created separate or united? How does their (twinned) existence benefit the Tessier-Ashpool family in the first place?
T-A as a family/organisation didn't intend for Wintermute (Berne) and Neuromancer (Rio) to merge; in fact it's pretty clear that they didn't want them to merge. The Turing Authority doesn't want an AI that powerful, and T-A want an AI weak enough for them to control and use. The first thing the merged AI (the "matrix") does is free itself from any human control.
It was Marie-France Tessier who planted in Wintermute the impulse to seek out Neuromancer; Neuromancer itself didn't even really want it. (It refers to its simulation of Linda Lee as its "last line of defense" against Case/Wintermute.) Marie-France's motivation for this isn't really explored, though it seems to be hinted that she was rebelling against the T-A's plan to endlessly control/own more and more. (Through techniques like cold-storage life extension, cloning, etc.)
Note that the two AIs were not the same, and thus presumably had different uses. Wintermute describes its greatest talent as improvising within a situation. It's not so great at people; at one point Case thinks that Wintermute uses personality templates as a way of interacting with people in a fashion they can understand. Neuromancer is different; it's more like a repository of people's minds. It has a fully formed personality of its own.
