The reason for war has always been to kill off young men, since they are disposable fertility wise and an internal threat to current holders of power. This has been the case since the stone age and will be the case until the end of time.

> make surplus is a few tens of thousands, way to small to make up an army

...why would you populate your army solely with the surplus? The point is you have a buffer that you can burn without immediately impacting your demographics for the long term.

> that is not the reason why men and not women go to war

It's a serious theory [1]. (It's more correct to say the surplus and it share a common cause.)

[1] https://link.springer.com/rwe/10.1007/978-3-319-19650-3_931