Why does it say that he ran after Eliyahu? It does not say that Eliyahu went away!
Radak: Indeed, Eliyahu took back his cloak and went.
Why did he run after Eliyahu?
Radak: Refer to 19:19:6:1.
Malbim #1: Elisha's soul clung to Eliyahu's cloak. He felt the spirituality that radiated on it when he was in the cave, like the veil on Moshe's face. With the cloak, Eliyahu split the Yarden (Melachim II, 2:8).
Malbim #2: Elisha was like the 12 oxen that hold up the Yam Shel Shlomo; Eliyahu's cloak is from the Yam itself. It was proper that Elisha go after him.
Why did he say "Shuv Ki Meh Asisi Lach"?
Rashi: Go back (from following me). What did I do to you (that you should follow me)? Radak - i.e. if I tilted my cloak on you, is this a reason to run after me?! He was testing if Elisha wants to follow him with all his heart.
