In Yona 4:4 why does God need to explain/justify what he did to Yona?
God isn't justifying himself to Jonah, he is justifying himself to us, thousands of years after the fact. We read the story of Jonah on Yom Kippur afternoon to remind us of the importance of repentance. Note that the people of Nineveh do not convert to Judaism, they merely cease their evil ways.
Jonah is one of the literary prophets, the prophets that wrote down their messages in books named after themselves.
"Is it right for you to be angry?"
Here, God gives an opportunity for Yonah to rectify his own sin, by causing him to reflect on himself. It is not God's intention to destroy, but to rectify us.
He is revealing to Yonah his own idol, the will.
He is not justifying what he did, he is asking Yonah an almost sarcastic question so that he can then go and show Yonah how silly it is for him to be so angry (with the kikayon).