Why does Gray have to kill END? In the recent manga chapters, Natsu is seen fighting Gray, from Natsu's side, he just wants to move forward to beat FT's enemies, and I understand that Gray received his magic to kill END, but exactly why does he have to kill END? Did they explain this and I missed the chapter?
The premise of your question is wrong. He doesn't have to. He wanted to. He wanted to kill END, but he actually doesn't have to kill END.

Okay, let me explain what I mean by the statement above. Gray figured that Natsu is END. Does he have to kill Natsu? No. Natsu was perfectly human at that time, and as long as he is human and have control of himself, there would be no reason for him to kill Natsu. Besides, at that time the Spriggan 12 is yet to be eliminated. Obviously Spriggan 12 is a bigger threat than END that is clearly on his side. So, once again, he doesn't have to kill END (at least not at that time) and he certainly shouldn't either.

But, Gray wanted to kill END. This is the difference. He wanted to kill END, because END is one of the Demons of the Book of Zeref. Gray is obsessed with killing all of Zeref's demons (and eventually Zeref himself) because Deliora has killed his family and later his master, Ur. He is motivated by vengeance, and this desires blinded him about the fact that END is a nakama. This is proved by Erza managing to stop him by making him remember that no matter what, Natsu is still Natsu.