Remember our friend adenosine, the sleepy molecule? I talked about it from my post a long while ago. Adenosine is a chemical that starts to slowly accumulate when you wake up, until it finally bonds to enough neuroreceptors to let you know it’s time to hit the hay. Caffeine works its energetic magic by competing with adenosine for neuroreceptor access.
In summary, you’ll remain alert until caffeine is finally metabolized, since the adenosine is no longer blocked off. How long it takes to metabolize caffeine is in our genes. There are two that affect this: AHR, which affects the production of CYP1A2, which breaks down the majority of caffeine in the body. One who metabolizes caffeine fast is very likely to get another cup, and perhaps another.
Slower metabolizers can probably make do with just one cup of coffee; anymore could bring discomfort that further discourages them from having more anyway. Since caffeine blocks adenosine, slower metabolisms may permit caffeine to linger too long, making it difficult to sleep, or to stay asleep. Caffeine is also known to elevate adrenaline levels, which further makes you more alert (and less able to sleep, if you’re at the point of day).
There’s other factors too, such as the taste of both coffee and caffeine; some people are simply averted by the [bitter] taste, even if sweeteners or creamers are in the equation (plus, that might be too much work for some). Information from 23andme & this Business Insider post.