well...That's the way he's portrayed in the bible.
'He is the Rock, his works are perfect, And all his works are just. A faithful god who does no wrong, upright and just is he.'
Deuteronomy 32:4
'As for god, his way is perfect; the Word of the Lord is flawless'
Psalm 18:30
'Then you will be able to test and approve what God's will is--his good, pleasing and perfect will.'
Romans 12:2
Okay, now we're getting somewhere

So your basis for God's goodness depends on the Bible.
Here are some more verses to consider:
"We accept good things from God, and should we not accept evil?" (Job 2:10)
"On a good day enjoy good things, and on an evil day consider: Both the one and the other God has made, so that man cannot find fault with him in anything" (Ecclesiastes 7:14).
Psalm 88.
The "Suffering Servant" portions in Isaiah 52:13-53:12.
"See now that I myself am He! There is no god besides me. I put to death and I bring to life. I have wounded and I will heal, and no one can deliver out of my hand" (Deut. 32:39).
"For he wounds, but he also binds up; he injures, but his hands also heal" (Job 5:18).
"For it is he who has rent, but he will heal us; he has struck us, but he willbind our wounds" (Hosea 6:1. This is taken out of context; but it seems to complement the quote from Job above.)
Throughout the books of the Prophets (and the Book of Deuteronomy to an extent), God is portrayed as deliberately inflicting suffering and exile upon his people. Now, this was seen by the prophets as part of a greater good (namely, to discpline and "cleanse" the people and make them turn back to God). However, it certainly didn't make the Israelites happy. So, your utilitarian theory, of the greatest good providing happiness, may not necessarily apply to God. My example of the child was for a situation such as, the child wants something like a big shiny knife. Now, the child loves the shiny knife and really, really wants it because he is convinced it will bring him happiness. Dad knows better and takes the knife away. Junior is devastated because his happiness has been taken away. Or, Junior really, really wants to eat the entire cake. He is certain that his happiness depends on this cake. And Dad takes it away citing tooth decay. Junior is devastated. He is certain his life is ruined.
It is only later on, when Junior matures and grows, that he realizes what a loving father he really had, and begins to understand why his dad did what he did.
The point I'm trying to make is............We don't really know what our own happiness depends on. We may think it's this job, or that person, or even our own health, home, finances, etc. etc. So, when those things are taken away, causing us to suffer, we rail against God -- not unlike Job himself. But the fact is that only God really knows what will bring our souls happiness in the long term; and God knows what he's doing. It certainly confuses us; it might not bring us happiness at this moment, or even in this life; but ultimately it is for our greater, long-term good. The progress of the soul is not the same as the progress of our bodies or even of our minds. The soul goes through an
eternal growth process. I believe that suffering has to be considered from this perspective.
Now, this is (a small part of) my own take on suffering that I have developed through my own life experience, and, yes, reading and studying the Bible. There are other excellent takes on suffering. Perhaps you would find the Buddhist ideas on the subject more approachable, or some other tradition
