Earlier quoted context omitted.
Because bitcoin is an algorithmic solution to exactly that problem - trust in a distributed system, casually known as the Byzantine Generals Problem, or Two Generals problem [1]. The innovators and early adopters were motivated by their understanding of the utility in finally achieving a solution to that problem in the context of digital currency (not historically possible for digital currencies till the invention of…
Just to nitpick a bit, the Two Generals problem is actually different than the Byzantine Generals Problem. 2GP deals with the (simpler) case of achieving consensus in a distributed system with unreliable communications. That is, messages can be reordered, lost or arbitrarily delayed, but end hosts are assumed to be trustworthy. BGP deals with the aforementioned scenario where nodes can be malicious as well.
[1]:https://en.wikipedia.org/wiki/Byzantine_Generals%27_Problem