It looked cool, but story was a bloated piece of work with some really lazy writing...
Lex Luthor hates superman. Why?...Because reasons of course. Anyone that can logically explain why...I'd love to hear it
Batman hates superman and wants to kill him. Why? Because he a sociopath and is apparently secretly manipulated by Lex
Batman has a workout montage before he goes out to fight Superman. Yep. This actually happens...
Batman spends most of the movie wanting to kill superman and then he stops at the point hes finally able to do so. Why?...cause they both have a mother of same name. Pfft...makes sense.
Lois Lane takes an important object and throws it down some deep well. Why you ask? Because there has to be an important scene later of her drowning that draws Superman away form the action.
Lex makes Doomsday by putting his blood in Zod’s corpse inside the Kryptonian ship which is just sitting around and is apparently still “37% functional". NSA and NASA apparently wants nothing to do with this ship...
The story has some issues although that may be due to the content cut from the theatre release like this scene.
1 - It's more a mental obssession with the Meta beings, Clark wasn't the only one Lex was after as seen with his tracking of Wonder Woman, Cyborg, Aquaman and the new wielder of the Flash force.
2- This is practically explained at the beginning, his dislike of him came from the collateral damage of the Zod fight where Batman not only became aware of his existence but sees him as a big threat to everyone on the planet after the Kryptonians tried to cleanse the Earth and the was nothing anyone could do not to mention a number of his friends and employees died during that event. Lex just added a bit more fuel to the fire.
3- This is more up to the viewers interpretation tbh.
4- She threw it because she didn't want it to be used against Clark in future, she and everyone else had no idea at that point that Doomsday was going to show up.
5- The ship only became operational because Lex accidently activated it, he needed government clearance to even go near it which he got by pulling strings.