I personally don't believe modern machine learning is remotely close to AI, except perhaps the very lowest rung of the ladder of self-serving AI definitions. I base that belief on what seem to be the unknowns, reinforced by predictable failures. But I have very little reason to believe it's impossible. Not even the possible necessity of quantum effects would seem to preclude it. Heck, we've already begun harnessing quantum effects in materials science, computing, biology, and other areas.
Unless you mean that whatever we could eventually come up with would be more biological than machine or that only a human could think like a human, but that seems more like word play, the kind of game AI believers play. (That said, that poses an interesting question: which is more likely to be achieved first--a designed-from-scratch, DNA-based cellular intelligence, or something not based on DNA or otherwise mimicking existing organic life? If at all, of course. Also presuming such a distinction isn't in fact hopelessly quaint and naive.)
 I'm not a naysayer. While I never believed self-driving cars were around the corner (not even 5 or 10 years out; you can Google my HN comments from years ago), I have no doubt the science has been useful and can and will and is put to great, largely unseen use, as is typical of most science.
We can't build a conscious machine because I believe there is a spiritual aspect to life that we have thus far failed to empirically observe or measure. Put another way, I believe all humans have a "spirit" inside of them, and that said spirit is a prerequisite of conscious thought. This same spirit is what makes life after death possible. This belief, of course, is an extension of my belief in God.
Thus, it is impossible to build a truly conscious machine without a spirit to inhabit said machine.
This all implies, of course, that truly conscious AGI effectively proves God does not exist since it proves there is nothing special about humans or any intelligent life for that matter.
In summary, since I believe there is something special about life and that there is a secret sauce (spirits) that we haven't observed or measured, AGI projects are always doomed to fail (though they may spawn new interesting fields of mathematics or computer science)
You're entitled to your belief, of course, but simply asserting the existence of [Christian] souls and an inter-relationship between souls and intelligence isn't sufficient to make your claim.
Discussing souls is probably not appropriate subject matter on HN, but I thought it was worthwhile to make the point that even religions can have and utilize the concept of unknowns to self-limit its theological reach. Technically speaking, orthodox (small 'o') Christians (Catholics, Orthodox, mainline Protestants) only need affirm the Nicene Creed and nothing more, just like, AFAIU, Muslims need only affirm the Shahada. Thus, an orthodox Christian is supposed to affirm the Trinity, the resurrection of Jesus, etc, but otherwise free to accept or reject machine souls, notwithstanding additional doctrinal strictures of particular denominations that might dictate a particular choice.
 This is why you see seemingly radical priests quoted as admitting that aliens could have souls. (And also why it's so easy for Bill Maher or Michael Moore to find a priest to make seemingly contradictory and outrageous statements; more often than not the priest is playing them more than Maher or Moore understand, they're just too cynical to appreciate it.) Catholicism is hardly the only religion, or even Christian religion, with such a concept. But it's perhaps gone to the greatest lengths to develop and integrate the concept with modern logic and science.