This is a generational hatred. Before Joram became king, there was another famine and another prophet in 1 Kings 18
1 After a long time, in the third year, the word of the Lord came to Elijah: “Go and present yourself to Ahab, and I will send rain on the land.” 2So Elijah went to present himself to Ahab.
Now the famine was severe in Samaria, 3and Ahab had summoned Obadiah, his palace administrator. (Obadiah was a devout believer in the Lord. 4While Jezebel was killing off the Lord’s prophets, Obadiah had taken a hundred prophets and hidden them in two caves, fifty in each, and had supplied them with food and water.)
Joram inherited the kingship after Ahab.
Elisha inherited the prophetship after Elijah.
Joram was the son of Ahab and Jezebel. He inherited the hatred as well as the kingdom. For this OP, one key is Jezebel.
1 Kings 19
1 Now Ahab told Jezebel everything Elijah had done and how he had killed all the [her] prophets with the sword. 2So Jezebel sent a messenger to Elijah to say, “May the gods deal with me, be it ever so severely, if by this time tomorrow I do not make your life like that of one of them.”
Jezebel was a strong character and wanted revenge by killing Elijah but she failed. She indoctrinated her son Joram as she indoctrinated her husband Ahab.
1 Kings 16:30 Ahab son of Omri did more evil in the eyes of the Lord than any of those before him. 31He not only considered it trivial to commit the sins of Jeroboam son of Nebat, but he also married Jezebel daughter of Ethbaal king of the Sidonians, and began to serve Baal and worship him.
1 Kings 21:7 Jezebel his wife said, "Is this how you act as king over Israel? Get up and eat! Cheer up. I'll get you the vineyard of Naboth the Jezreelite."
So, Joram found it expedient to blame Elisha for the siege and famine because of his mother Jezebel's influence.
There is a strong parallel between Ahab-Elijah and Joram-Elisha including lastly the endings of the famines.
1 Kings 18:41 And Elijah said to Ahab, "Go, eat and drink, for there is the sound of a heavy rain."
2 Kings 7:1 Elisha replied, "Hear the word of the LORD. This is what the LORD says: About this time tomorrow, a seah of the finest flour will sell for a shekel and two seahs of barley for a shekel at the gate of Samaria."
The famines ended with both Ahab and Joram enjoying eating and drinking upon the words of Elijah and Elisha.
There are no reasons for these kings to hate these prophets except by the influence of Jezebel.