You don't have to explain much in sociopathy.
Read Understanding the Sociopath: Cause, Motivation, Relationship, in "Psychology Today." An excerpt:
In the media, I'm often asked what causes sociopathy. "Are they born this way?" is one of the most frequently asked questions. The truth is that we don't know. Stout (2005) sums up the research well, explaining that as much as 50% percent of the cause of sociopathy can be attributed to heritability, while the remaining percentage is a confusing and not-yet-understood mixture of environmental factors. (Notably, a history of childhood abuse among sociopaths is not always present.) Similarly, Ferguson (2010) conducted a meta-analysis and found that 56% of the variance in Antisocial Personality Disorder, the formal disorder of sociopathy, can be explained through genetic influences.
Emphasis mine. Basically, sociopaths can be born with the capacity to be sociopathic, and that can be triggered by childhood trauma, but does not have to be. They can just make selfish decisions throughout life and be sociopathic because they were born with a diminished capacity to feel love, friendship, etc.
Now there are dissenting opinions on this point; some say only psychopaths are born that way and sociopathy is a result of culture. If you find them (like this one from the same magazine) I would point out that the excerpt I quoted has an actual scientific study behind it, and the articles claiming otherwise have no science, they are psychologists giving an opinion of how to define "psychopath" v. "sociopath", while ignoring the evidence of heritability in sociopaths.)
Sociopaths see other people as objects to be used. They don't really become "infatuated," but they may become obsessed with owning somebody. The difference is, a sociopath uses them like most of us would use any tool, without regard for whether the tool is tired, hurt, sad, or afraid. They use the women they own for sexual gratification, pride of ownership and proof of their own virility and attractiveness (she's a super model!), even their children are objects groomed to prove their own superiority.
The proper motivation of your narcissistic sociopath is not "infatuation" with another but love of themselves and their own desires for power, sex, money, and an obsession with other people's admiration. If they give gifts, it is to force admiration. Their desire to own the MC, have her obey their commands and satisfy their desires.
It sounds like you are trying to create "sympathy" in your sociopath for your MC's upbringing, and this is a mistake in writing. It is common, even in published writing for print and screen, but not how sociopathy works IRL.
For anybody writing a sociopath, their motivations are about themselves, which can be anything from private sexual gratification to public admiration, power to compel others to do what they don't want or hate doing, the power of breaking up romances or marriages, etc. Life is a game and they are winning it.
To make your MC an attractive acquisition, think of her as a possession he can point at: You can make her beautiful, of course. But you can also make her skilled, so he can be proud to own her (like owning a champion dog). Or unusual in some other respect; a battlefield hero (yes women can be that), a genius, a person of fame due to some other circumstance.
For some reason she attracts his attention and he want to own her. That's all you really need, if you show all his other relationships are just as manipulative and self-serving.