Why did Lord Voldemort want to kill Harry Potter and his father only?

Answer 1

Because of the prophecy that was revealed in the 5th book: The one with the power to vanquish the Dark Lord approaches… born to those who have thrice defied him, born as the seventh month dies … and the Dark Lord will mark him as his equal, but he will have power the Dark Lord knows not … and either must die at the hand of the other for neither can live while the other survives … the one with the power to vanquish the Dark Lord will be born as the seventh month dies … It could have applied to Harry or to Neville, but Voldemort thought he was fulfilling the prophecy by killing Harry.

Answer 2

Initially Voldemort wanted to kill only Harry, he couldn't care about his parents. The reason for this was Harry was the only one in the way of Voldemort's power, hence he only cared about killing Harry.

he then killed James Potter because he was standing in the way. He killed Lily Potter because she too was standing in the way. There was no mention of him specifically planning to kill all 3 Potters, with Harry being the first or second to die.

Answer 3

Human life meant nothing to Voldemort, the only reason he was willing to spare Lily was because Severus Snape asked him to as he was deeply in love with her.