It's a relatively hyperbolic assertion that Bitcoin will end war, like, "Fix the money, fix the world." But it holds a lot of truth because people are largely motivated by the rewards of the systems they are immersed in relative to their perceptions.

Fiat currency incentives war because it's a blank check for those who control the money printer, that is, it's an incentive for bad ideas because reality punishes bad ideas, but for a brief time people can personally avoid the consequences of their currency printing and war mongering by robbing the value of their currency through currency debasement. When governments can't use their money printer to finance their bad ideas, including war, then they are forced to turn to other forms of resolving conflicts or solving problems besides using force and/or fear.

Historically money/treasure/valuables or currency has been physical in nature, which incentivized violence because if I kill you, I get your stuff. Now, if I kill you and you hold most of your value in Bitcoin (spiritual money) rather than a house or goods or cars, I don't get your value, which is a disincentive to violence.

But also, in the long run since government will be financed by proof of work and influence and not coercion, the Bitcoin system will gradually incentive character and competence in government, both local and national, because it will be easier to defund and fire and geo-arbitrage out of the jurisdiction of those who make poor choices based on bad ideas. Government in this Bitcoin incentivized system, will no longer be a monopoly, and will be compelled to compete for citizens by setting up conditions that are favorable to their constituents.

Furthermore, as more countries and localities and companies and families go on the Bitcoin standard, waging war against another government would become waging war against another party using Bitcoin, which violates self-interest because they are using the same monetary system. It's the opposite of what Ayn Rand said, which is something like nations that don't trade goods will trade bullets. Since nations will trade goods and Bitcoin, they won't trade bullets.

Bitcoin turns enemies into allies.