[HarHarVeryFunny]

My mental model is of each side (think left/right in 2-D) of the iceberg competing with the other side to float to the surface by rotating the iceberg around it's center of gravity. The only stable positions are where these left/right rotational forces are balanced.

If an iceberg is currently floating in a vertical orientation where more of it's mass to one side of it's center of gravity (bottom half) is underwater compared to the mass on the other side (top half), then it's going to tend to rotate until both sides are equally above water, so (depending on mass distribution) horizontal orientations are likely to win over vertical ones.

Of course an iceberg could balance vertically, but that's like balancing a pencil on your finger - not the most stable, and any disturbance (such as the initial calving event) is likely to rotate it into a more stable horizontal orientation.

[Sharlin]

That’s exactly it. An iceberg can’t stay "vertical" for the exact same reason that a pencil can’t stay vertical. Even if perfectly balanced, the equilibrium is unstable.