At first, I really want to get to know you. This is because I don't know you as well as I ought to. I will proceed to get to know you.
At a certain point, whether this is an hour after we've met, two days, two weeks, a month... I will reach a decision point.
Either you are a person that I am interested in getting to know further, much more deeply, or you are a person I am content to remain at this level of knowledge of, or you are a person that I should not know this well.
Based on this, different things will happen.
If I am interested in getting to know you further, I will continue to pursue deeper knowledge of you, sharing deeper information of myself. If I am content to let things remain as they are, I will remain cordial, but further in-depth information about me will not be forthcoming, and I will cease efforts at getting to know you better. If I don't wish to know you that well, I will be actively cool and actively discourage efforts on your part to continue to know me.
(Sadly, some people I don't know that well who I have no interest in knowing further but do wish to maintain contact with may interpret my cessation of getting-to-know-you-better activities as active discouragement of further contact. I'll be working on how to make my actions not as easily misinterpreted in the future.)
But, if I am in a romantic-type relationship with someone, and have no wish to know them further... that relationship is Doomed. Not because I am not giving them a chance, but because they have completed the period of initial testing, and I am just not interested in getting to know them more deeply.
That's not to say that I don't get to know friends-I-don't-need-to-know-more-about deeply. It's just not a drive. If it happens, it happens, but that sort of thing accretes through continued contact, rather than being actively pursued by all parties.
I have never been able to continue a romantic relationship with someone that I don't wish to know any better. No fault of theirs: I'm just not interested. Fuckbuddies, fine. Dating, no. But the spark usually goes out of the sex...