IANANR (I Am Not A Neuro-Researcher), but it seems to me the "only" step you're requiring is that of self-consciousness. We can explain why we think it's an ostrich because we can point our neural networks at themselves, and say, "what sort of thinking process does this look like? Oh, it looks like visual pattern recognition of certain features like a long hairless neck, bird features, etc, so that's why I think it's an ostrich."
We are capable of conceptual thinking because we can think about our own thoughts, and further think about our own thoughts about our own thoughts, etc, in an endless cascade of meta-thinking (which is in fact what thinking is). The ability to experience a gestalt, and the ability to think about it, are two major steps. We seem to have achieved the first, with current NNs. That's pretty amazing already!
I think the ability to be pointed at itself is a necessary step for those NNs to develop self-consciousness and, thereby, conceptual understanding. We're not there yet, for sure, but how much further are we? A few years? A decade? A few decades? The latter is no doubt a very pessimistic estimate (conservative AI researchers agree on this).
Human-style intelligence is certainly not here yet. But it is almost certainly just around the corner.