Pinker wants to establish metrics to evaluate the state of the world. Once he establishes the metrics, he wants to show that the state of the world is improving over time. Showing improvement by these metrics, he wants us to celebrate this. This is easy to appreciate. He is right. There really are large differences in living and these differences are commonly experienced as better. There is real cause for celebration and continued efforts at improvement. If this were all he was doing, his book might be universally praised.

But despite the truth of his cited facts, Pinker makes many common errors in reasoning when he attempts to claim sweeping philosophical conclusions from his series of empirical observations.

You can see Pinker's faulty thinking in his attempt to define progress:
"What is progress? You might think that the question is so subjective and culturally relative as to be forever unanswerable… Most people agree that life is better than death. Health is better than sickness… All these things can be measured. If they have increased over time, that is progress."

Progress may exist. It is not established by whether most people agree on something or not. That the majority believes something to be the case, does not make the thing the case. It does inform us, namely of how humans experience the something but it does not establish the something to be the case.

He repeats this error moments later:
"Granted, not every one would agree on the exact list."

Whether every one did agree on the exact list wouldn't change the situation. That 100% of Earth believed X would not make X the case.

He follows this with a fallacy:
"If you’re reading this, you are not dead, starving, destitute, moribund, terrified, enslaved, or illiterate, which means that you’re in no position to turn your nose up at these values."

This is a cute display of polemic but not a valid argument. The fact that I can read, does not establish that reading is good. Reading may be good but whether reading is good or not is not at all determined by whether I can read or not. His sentence here is something that seems that way but is not true (my freedom does not establish what I must value).

He continues with his previous rule-of-majority error:
"As it happens, the world does agree on these values. In the year 2000, all 189 members of the United Nations, together with two dozen international organizations, agreed on eight Millennium Development Goals for the year 2015 that blend right into this list."

Again, even if all 7 billion people expressed that they believe "murder is wrong" this would not establish that murder is wrong.

This isn't to say that murder is not wrong. It's just to say that pointing out what humans do cannot establish what is wrong. Murder is wrong objectively (independent of human minds and their opinions and perceptions) or it is not wrong at all. Anything else is merely observation of what humans happen to hold or happen to practice. Pinker, Sam Harris, and others on the TED stage attempt to ignore this troublesome hindrance to the worldview they promote, dismissing it with a wave of their hand when it is raised and moving along with their presentation. The widely-held feelings and sentiments of humans everywhere do tell us something, just not what Pinker and Harris suggest: there is an intrinsic understanding of right and wrong in every human and we should pay attention that this is present. But this doesn't change the situation that values are objective realities or they are merely subjective whims/emotions/opinions (and may be treated like all other whims/emotions/opinions: ignored).

Pinker as a discussion of what is happening–fine, useful, needed. Pinker suggesting both that many values many humans happen to hold should be held and on this basis and that those who notice this is not philosophically sound are simply pessimists–laughable.