Why does God have to be "perfectly good"?
Because God is pretty much defined as a perfect being, who is perfectly good. If there exists something which resembles God in other ways but isn't perfectly good, then it's not really God (it is, perhaps "a" god, but that's not the same thing). A god who isn't perfectly good would be unworthy of worship, for example.
Also, theists typically (though not universally) think that God is the source of morality, such that whatever God says is good (or does) is good by definition. On this view, God has to be perfectly good, because he defines what is good.
Doesn't this presume an anthropocentric view of God - a god whose intentions and actions conform to the human notion of good, which seems to be just what is good for human beings?
Theism is essentially anthropocentric, since theists believe that the values that human beings have are somehow fundamental to the universe. To say that the universe is created and maintained by a good God is to say that our distinction between "good" and "bad" is real and (literally) universal. Of course a theist isn't committed to the view that God's values are exactly the same as ours, or that what God considers good is exactly what we consider good. Most theists would deny that to some degree. But there has to be some overlap or similarity between the goodness of God and what we understand by "good", or there'd be no point using the word "good" to describe him at all.
Human beings are only a small part of creation. If creation is what it is.
In the immensity of time and space, why would human beings (in this tiny part of space, and this incredibly narrow window of time) figure at all greatly in any of God's calculations? A being, presumably, of infinite expanse and duration.
The theist's claim isn't that God takes our values into account, it's that our values derive from God. It is God who is primarily good, and our understanding of goodness is based on that, however imperfectly. Perhaps there are other beings elsewhere in the universe who also derive their understanding of goodness from God, in which case they'd have similar values to us.
All of this is going rather off-topic, though.