At the same time I noticed that the majority of engineering managers, product owners and agile coaches in our company are women. Some of these women were programmers at some point in their career.
I'm not deducing anything from this (especially since it’s a single datapoint) but it sure is interesting.
Are you actually counting how many of you are woman and conclude based on that, that you are better off than other companies?
It's not low, or high, or medium. It just is. As long as you are not rejecting perfectly capable women/females (just because they are so), you are not doing anything wrong and you are not worse off.
Many women get nudged/pushed into middle management instead of promoted to technical leads or directorships. It's often a way for companies to claim they "promote" women, while forcing them into roles that are vulnerable to layoffs.
Since an Engineer may change jobs half a dozen times over a career, but women generally change once (to non-Engineering job) we have a cumulative effect.
I don't understand this reasoning. Are you saying that women generally have one engineering job and then they change to a non-engineering one? If not, where is the number difference coming from?
Off-topic: why do you capitalize "engineering"?
I capitalize Engineer as an occupation, like Doctor Smith. Yeah, probably don't want to capitalize it as an adjective.