In Nightcrawler, Jake Gyllenhaal's character, Lou Bloom, has noticeably strange mannerisms as well as (arguably) a lack of empathy. What could be the reasons for this strange behaviour?
As adressed in this related question his character first and foremost seems to be a sociopath (or psychopath, whatever you call it) in that he lacks any kind of empathy for other people, as you indentified it yourself. But the question remains why he is that way. That is a question though, that unfortunately often is not too easy or definite to answer. But Nightcrawler's overarching motifs might give us some hints as to why Lou Bloom is such a cold person.
For that I'd yet again employ one of Wolfgang Schmitt's interesting analyses (unfortunately not available in English), who sees the movie not so much as media criticism but rather as commentary and criticism of capitalism and that Lou Bloom as a modern successful businessman is the embodiment of that capitalistic system:
Now the media criticism isn't new and it would be easy for the audience to morally raise themselves over this and say "yeah, that's bad that such sensation news exist" and then everything would be fine. But director Dan Gilroy is not concerned about a bit of moral and integrity, but about a systematic criticism of capitalism, hinged on one example. It would be far too easy to say "Jake Gyllenhaal amazingly plays a psychopath who uses every possible means to get bloody image material. The character is crazy and with this craziness he can make good money." But that goes too short, for here do the great dialogues come into play. Because this supposed psychopath Lou speaks in the language of economy. Everything he says he has from success guidebooks, business online courses, theories of supply and demand. He doesn't use this coaching and management language emphatically, as he saw it in The Wolf of Wall Street, but rather completely factually and levelheaded. The considerateness with which he justifies that he pays his employee a starvation wage, why he wants to have sex with the TV editor, and why he betrays the police, all that makes the abysmal of this character. This abysmal reaches beyond a psychopathology. He is not a psychopath, he is the embodiment of the capitalistic laws, and that in its purest form. We have an I that constitutes itself by the rules of economy. [...] Lou as personification of capitalism is one of the most original characters of this cinema year...
...All relationships in this movie, even the "love" relationship, are founded on supply and demand and the government is only seen as powerless police, for the power is entirely privatized. [...] The economic pierces through everything, especially when he tries to hook-up with the editor we see what we call today a "pick-up artist", he is exactly that, he internalized the economic rules of supply and demand and can also manage his private relationships that way...
Lou is a mixture of Norman Bates (who himself was no businessman and had a motel far away from the stream of money) and the photographer from Blow Up (who himself as a cold person brought enough amorality for the business). Starting from Hitchcock and Antonioni, Gilroy converts the voyeurism discourse into the capitalism discourse.
If we take this characterization of Lou as a businessman and capitalist par-excellence, we can make some speculation of why he is that way, be it just by the stereotypical statement that he is just a perfect product of his environment and its zeitgeist. Lou has perfectly realized and internalized what one needs to be successful. He is pretty much a self-taught member of the Generation Internship as he himself says when he "applies" for a job at the beginning of the movie:
I know that today's working culture no longer caters to the job-loyalty that could be promised to earlier generations.
Lou comes from a system where you have to accomodate to its amorality and short-lived world in order to be successful. He has realized this long ago and applies exactly those rules. You could say he is the American Dream gone extreme. Now it is surely a certain lack of empathy in his character in the first place that lead to this development, but the system he tries to survive and succeed in actively embraces and encourages this lack of empathy. Like this system he is not so much immoral rather than amoral. And it is his success that confirms him in the end.