This has been my field of research. I've seen the previous answers that suggest that we don't have sufficient computational power, but this is not entirely true.
The computational estimate for the human brain ranges from 10 petaFLOPS (1 x 10^16) to 1 exaFLOPS (1 x 10^18). Let's use the most conservative number.
The TaihuLight can do 90 petaFLOPS which is 9 x 10^16.
We see that the human brain is perhaps 11x more powerful. So, if the computational theory of mind were true then TaiHuLight should be able to match the reasoning ability of an animal about 1/11th as intelligent.
If we look at a neural cortex list, the squirrel monkey has about 1/12th the number of neurons in its cerebral cortex as a human. With AI, we cannot match the reasoning ability of a squirrel monkey.
A dog has about 1/30th the number of neurons. With AI, we cannot match the reasoning ability of a dog.
A brown rat has about 1/500th the number of neurons. With AI, we cannot match the reasoning ability of a rat.
This gets us down to 2 petaFLOPS or 2,000 teraFLOPS. There are 67 supercomputers worldwide that should be capable of matching this.
A mouse has half the number of neurons as a brown rat. There are 190 supercomputers that should be able to match its reasoning ability.
A frog or non-schooling fish is about 1/5th of this. All of the top 500 supercomputers are 2.5x as powerful as this. Yet, none is capable of matching these animals.
What exactly is the obstacle we are facing?
The problem is that a cognitive system cannot be defined using only Church-Turing. AI should be capable of matching non-cognitive animals like arthropods, round worms, and flat worms but not larger fish or most reptiles.
Edit: I guess I need to give more concrete examples. The NEST system has demonstrated 1 second of operation of 520 million neurons and 5.8 trillion synapses in 5.2 minutes on the 5 petaFLOPS BlueGene/Q. The current thinking is that if they could scale the system by 200 to an exaFLOPS then they could simulate the human cerebral cortex at the same 1/300th normal speed. This might sound reasonable but it doesn't actually make sense.
A mouse has 1/1000th as many neurons as a human cortex. So This same system should be capable today of simulating a mouse brain at 1/60th normal speed. So, why aren't they doing it?