Why is Vegeta's life-long obsession/rivalry with Goku?

[KBABZ]

I`ll venture that up until a point, the rest of the cast did have the desire to be better but they did the same mistake Vegeta does (look at Tenshinhan, virtually preparing his strategy in the 23rd Bodukai focusing on how his previous match with Goku went), the only difference is, as soon Super Saiyan is introduced, any hope of doing so is burnt to the ground whereas Vegeta having the same physiology stands the better chance.

The irony is that the supporting fighters have all become so much stronger than their past selves; if Tien could see his performance against Cell after the 23rd WMAT, I bet he'd be less inclined to hang up his coat.

[Anonymous Friend]

My take is that, while Goku has never beaten Vegeta, the mere fact that a lower class nobody on some backwater planet who was getting curbstombed in a 2v1 fight with Radditz is forcing him to go Oozaru. Then he has the gall to spare his life once his group defeats him. Then the next time Vegeta encounters Goku, he's really feeling himself. He's just dropped Freeza's lieutenants and one of the Ginyus. But hits the wall with Recoome. Goku shows up, Nappa'd Recoome, and whoops Jeice and Burter. The only reason Vegeta was as focused on Goku yet was because he still had to deal with Freeza. The he dies and comes back to the Super Saiyan.

Vegeta leaves earth, comes back just as Freeza returns. There's an unknown Super Saiyan, plus Goku now. Later, once he finally becomes one himself, the ability is outclassed. Then his enhanced self is made worthless.

All in all, I think that Vegeta was just looking to go to Namek to make a wish and go back to kill Goku and be done with it. But at every step there was so much stuff sidetracking him. The only chance he had would have been after Cell, but then Goku was dead. Then he started seeing his final chance getting away with the Babidi nonsense and had to take his moment to get his dignity back.

[Ripper 30]

It has all got to do with Vegeta's Pride. he grew up thinking he is the mightiest Saiyan Alive so when he met Gokū and got beaten by him he was shocked because he had pride in his elite skills and Gokū was a low class warrior so that's why it was too much for him and after he saw that Gokū reached the Legendary SSJ Form before him was even more frustrating thus he promised to himself that he will surpass Gokū one day.