When a government coalition is formed, each party gets some specific positions, and it's generally free to choose who to appoint. Within each party, gender balance and geographic balance tend to be important, as the voters are otherwise likely to punish the party in the next elections. Some people also have personal priority, for example because they are in the party leadership or they reliably bring in a lot of votes.
Not all minister positions are equal. Some (such as those dealing with economics, finances, and foreign policy) are important, while others (such as education and culture) tend to be low status. Top positions go to high-priority people, while low-status positions are often given to people with specific combinations of traits.
Defense has been a low-status position in Germany, largely due to political culture shaped by losing WW2.
Unless you're assuming that women are by nature less competent, narrowing to half of the population either includes the best candidate or at least one infinitesimally close to the best candidate with ridiculously high probability.
So what's the harm exactly?
The benefit is that we actually end up with some diversity, instead of the usual old-white-guy club that most of the West defaults to in leadership positions.
My response would be that that's great but I don't see what the plus part is bringing to the table.
I'm slightly more familiar with the U.S. side of things and clearly woman get the shaft - mainly because senior positions tend to pull from areas (fighter pilots and SOF for example) where the applicability of those particular experiences to command compared to other areas is at least questionable.
I think the answer to that problem is to see if the premise - running around in the boondocks leading a platoon in extremely high pressure situations or flying an F-35 off a carrier deck is relevant experience for a 4 star general or admiral - is true or if there's not equally or more relevant areas of expertise. Not - let's have people with different experiences because it's different.
Probably. Even if the decisions made are 100% the same, or at least equivalently valuable, it has benefits throughout society because it makes people everywhere feel more included, and it gives children the idea that they too can do what they want.
If you're a woman or person of color or etc. and relatively _nobody_ in leadership positions has anything like your life experience, and none of them look anything like you, what does that do for either your impression of how the organization aligns with your interests, or your desire to try for a career in whatever organization? Nothing good.
> If they were to say - "We have a candidate with a bold new vision for the armed forces of Germany; they bring things to the table unlike anyone else - plus they're a woman."
Those are not completely unconnected things. If your baseline is 100% old white men, someone who is not in at least one of those categories is likely to have different approaches and ideas that may be worth considering.
So your question is a bit problematic to answer honestly, because it explicitly assumes that the diversity of experience part is 100% divorced from the diversity of thought part.
The much more sane way to do it would be to just drop the female variant and retrain people over time to no longer infer a natural sex from the grammatical sex. We even already do this in cases where there are no natural sex specific variants, der Mensch means human, grammatically masculine but no one derives from that that we are talking about a man. Die Leiche means corpse, grammatically feminin but no one derives from that that we are talking about a woman. And if you really have to differentiate, then you can always use adjectives, der weibliche Lehrer, der männliche Lehrer, the female teacher, the male teacher.
On the other hand, the MoD has been the red-haired stepchild of ministries in Germany for a long time, especially when left-wing parties control the government. You could almost think that they are intentionally trying to sabotage it by putting people in charge who are completely unqualified. Lambrecht is just the latest example of that. Then again, Merkel didn't do much better.
Lambrecht's direct predecessor under the Merkel administration was not much different. Her predecessor became President of the European Commission after Merkel had to get her out of dodge due to a scandal that had resulted in a parliamentary inquiry.
Her predecessor made decisions that were directly responsible for a lack of spare parts as well as a failed programme for developing the "Euro Hawk" drone.
His predecessor's political career was ended by a plagiarism scandal involving his PhD thesis.
And so on...
I know it's innocous and unintended, but using this expression causes all kinds of problems to red-haired kids (I imagine as an adult you can get fed up with some references, too).
[1] apart from politics where the situation is oddly enough reversed