How is Yahweh not immoral?

[Aractus]

Whenever a story of god's immorality surfaces, one of the following apologetic arguments is used as a retort:

1. That was the OT.
   
2. You just don't understand the customs of the day.
   
3. Who are you to judge god?
   

Let's look at the first one. What did Jesus really say?

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Matthew 5:17-20
17 “Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18 For truly I tell you, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. 19 Therefore anyone who sets aside one of the least of these commands and teaches others accordingly will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven. 20 For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven.

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He does not appear to have made any attempt to overturn them. Now, what if he did overturn them? This could only mean that god had made imperfect laws before.

A pretty weak straw man argument...

Now, we will examine the second defense. This defense hurts its own argument more than it helps. If the laws of the OT coincide with the inferior moral views of the day (i.e. slavery permitted, semi-regular mass murders, etc.) then this is more evidence that they were created by human minds. After all, Jesus said

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Ephesians 6:5-8
Slaves, obey your earthly masters with respect and fear, and with sincerity of heart, just as you would obey Christ. 6 Obey them not only to win their favor when their eye is on you, but as slaves of Christ, doing the will of God from your heart. 7 Serve wholeheartedly, as if you were serving the Lord, not people, 8 because you know that the Lord will reward each one for whatever good they do, whether they are slave or free.

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Who are we to question his infalliable wisdom?

No, Paul said that and his scribe wrote it down, Jesus didn't say what you just quoted.

Picking and choosing the parts of the Bible when God is angry is not going to help your argument. Consider John 14:6-11 (Jesus did say this one FYI):

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Jesus said to him, “I am the way, and the truth, and the life. No one comes to the Father except through me. If you had known me, you would have known my Father also. From now on you do know him and have seen him.”
Philip said to him, “Lord, show us the Father, and it is enough for us.” Jesus said to him, “Have I been with you so long, and you still do not know me, Philip? Whoever has seen me has seen the Father. How can you say, ‘Show us the Father’? Do you not believe that I am in the Father and the Father is in me? The words that I say to you I do not speak on my own authority, but the Father who dwells in me does his works. Believe me that I am in the Father and the Father is in me, or else believe on account of the works themselves.
(John 14:6-11)

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If the character of God is as immoral as you claim, then you would be able to prove it by showing everyone that the character of Jesus is immoral. But if, on the other hand, you find that the character of Jesus is moral then it can only mean that the character of God is moral. I look forward to seeing you address this specifically.