This is an interesting questions, and it sould be part of the serene pantheon of AH memes.
Seriously, High Imperialism is a weird thing. There was no palpable trigger for starting it, it did not create much more wealth for the colonial powers, it hardly improved their military situation to "own" vast empty grass lands in addition to a valuable coastal city; although it gave opportunity to get at loggerheads, the main conflicts were created in Europe itself or could at least have been triggered there alone.
In short, it did not make sense.
So it has to be explained as a fashion. I can see three main reasons why this fashion trend has become so popular:
1. Aggression by the underdog. A defeated nation, like France after the Franco-Prussian War, seek other fields to prove its greatness.
Later, the rising power Germany tried to prove being on par with Britain and France by pushing into the colonial business.
2. Thoroughness. Doing things completely and to the end was considered a general task, in technology as well as in politics. The era was especially good at codifying laws and rules for international relations - thinking this to the end, you will have to know which toll office to inform about an issue on the Congo river.
3. Neurosis for military shocks. This time, especially Britain.
Britain built roughly half of its Empire out of the fear that someone could cut their traffic lines to India.
So, I guess you would need to suave these three items a bit ... good luck.