Why was Barty Crouch Jr. going to kill Harry?

Question

At the end of Goblet of Fire, after Harry returns to Hogwarts from the Little Hangleton graveyard and tells everyone that Voldemort has returned, Barty Crouch Jr. who's masquerading as Alastor Moody, acts in a rather puzzling manner.

His mission was to ensure Harry arrive in the graveyard at the time for Voldemort's rebirth ritual and he has completed it. Although Harry escaped, being a loyal Death Eater, Barty obviously knows that Voldemort would want to personally finish Harry off because Voldy's an ego-maniac, and the best way is to retain his cover and develop another plan. Instead, he takes Harry into his teacher's room, and points his wand at Harry. He mentions that Voldemort hasn't managed to conquer/kill Harry and now he'd do it himself.

'The Dark Lord didn't manage to kill you, Potter, and he so wanted to,' whispered Moody. 'Imagine how he will reward me, when he finds I have done it for him. I gave you to him – the thing he needed above all to regenerate – and then I killed you for him. I will be honoured beyond all other Death Eaters. I will be his dearest, his closest supporter ... closer than a son ...'

"Mad, am I? We'll see! We'll see who's mad, now that the Dark Lord has returned, with me at his side! He is back, Harry Potter, you did not conquer him — and now — I conquer you!"

[HP GoF - Chapter 35 Veritaserum]

Wouldn't Barty killing Harry would disturb Voldemort's end goal?

Answer 1

He clearly thought it would endear him to Voldemort, someone he had always been faithful toward... even to the point of going to Azkaban rather than renouncing him. Your own quoted text indicates that clearly:

I will be honored beyond all other Death Eaters. I will be his dearest, his closest supporter ... closer than a son ...'

Remember, Crouch Jr. wasn't present at the graveyard, so he doesn't know how badly Voldemort wants to be the one who kills Harry. This is a very common trope in fiction, where a henchman thinks they're helping/pleasing their boss by doing something, and that they'll be rewarded, when, in reality, the boss actually doesn't want them to do that thing and typically ends up punishing them.

Wouldn't Barty killing Harry would disturb Voldemort's end goal?

I'm not sure what you mean by his 'end goal'. His immediate goal at the time was to regenerate his body, which was already done by the time this scene between Crouch Jr. and Harry takes place. Voldemort's secondary goal was also accomplished (as part of the method chosen for reconstitution): he was able to use some of Harry's blood to regenerate, removing the source of Harry's protection from Voldemort:

When dear sweet Lily Potter gave her life for her son, she provided the ultimate protection; I could not touch him. [...] But things have changed. I can touch you now.

_{This is movie dialogue based on my recollection. The actual dialogue (and book dialogue) might differ a bit}

Of course, he still doesn't (and never does) know that Harry is also still protected as a Horcrux containing part of Voldemort's soul from that fateful night as well. For much of Book 7, he also had protection via the Elder Wand's allegiance. There's also the never-well-explained "golden flame" incident during the escape from the Dursley's, which was chalked up to some 'recognized connection between Harry and Voldemort through Harry's wand'.