With one water molecule we don't have any properties like 'wetness' or 'boiling point'. When we put a bunch of water molecules together, they now have new emergent properties and we have water.
If "A is A" how come, bunch of 'A's can have properties that no 'A' separately can have before!? These emergent properties can't be explained by mere actions/arrangement of bunch of 'A's.
Another simple example: hydrogen molecules & oxygen molecules combine to form water. We can see plenty of examples for "whole is greater than sum of its parts" in the study of Emergence It seems 1+1 is not just 2, something bigger than 2 happens in the above examples.
How does objectivism handle the above question!?
The Law of Identity only says that everything is what it is, whatever that is. Or: A is A, for any/each A. To see emergent properties as violating Identity, you would need to equivocate on what you are talking about the identity of -- so clearing up that equivocation should clear away the seeming puzzle.
My favorite example of emergence involves half-spheres that are magnetic on the flat side. A half-sphere has an identity such that, on a flat surface like the bottom of a box, you would find it exhibiting either stillness (flat side down), or wobbliness (curved side down). Throw one in a box and you'll find it exhibiting one of these two properties.
Now consider a system with lots of them at once, like putting several in the box and shaking it up a bit. You'd expect to see the above stillness and wobbliness, for sure. But some pairs could also end up flat-side to flat-side, forming a sphere. Ooooh, in that case we'd see rolliness in the box, which is neither stillness nor wobbliness -- that's an emergent property of systems of half-spheres!
Notice that nowhere in the above description will you find a half-sphere acting in some way contrary to its identity. The stillness and the wobbliness are expressions of a half-sphere acting alone on the bottom of the box. And the rolliness we see when half-spheres come together is likewise an expression of the identities of those half-spheres (when acting in concert). Again, no violation of identity.
You can only see a violation of identity here by conflating the properties of the system for properties of the system's constituents. Just keep straight what you're talking about the identity of at any given time, and the puzzle goes away.