I have noticed that quite a few people who deliver these types of training are wholly unaware that this terminology is offensive. They've had training from only one interest group, they've been told this is inclusive and they have never heard a diverging opinion.
So, if possible, I would start engaging by asking if they are aware that this terminology is offensive. And then explain why it is dehumanising to women and girls to be reduced to and addressed by bodily functions.
Moreover, the terminology is - as pp have noted - inaccurate.
99.9% of girls go through menarche (that is they have their first period). There is always an underlying medical reason when this does not happen by about age 15. This is called primary amenorrhea and rare. Treatment may resolve the issue.
The prevalence of secondary amenorrhea not caused by pregnancy, breastfeeding or the menopause is about 3 to 4%. Treatment may resolve the issue.
Menstruation is about as universal a female experience as you can get. The only other female experience as universal as menstruation is probably the fear of male violence.
So, only women and girls can menstruate but at any given moment in time, only about 25% do. Not only because they are too old, too young, pregnant, breastfeeding, ill, stressed, under- or overweight, on certain types of birth control or suffering from any number of medical conditions preventing menstruation, but also because menstruation is cyclical and on average limited to one week in four.
A great many of these women and girls are not "people who menstruate". Because they don't. They may in the future, or they may have done in the past, but if you are addressing training to people who menstruate, you're not addressing it at as large an audience as an educator typically would seek to do.
As a non-native speaker, I'd also like to add that there are many more women and girls whose first language is not English and who would not understand this terminology than the number of women and girls who identify as trans.
There are also many more women and girls who lack the cognitive capacity to easily understand the phrase. "Women" and "girls" are well-defined words, clearly delineated and easily understood. They grab your attention if you are a woman or a girl, because you immediately know this is about or for you.
"People who menstruate" does not grab your attention. Because the first word is people, our brains do not react in the same way. By the time you get round to "who" and "menstruate", a great many women and girls will already have decided that this isn't for or about them anyway.
So by using this terminology, you are not just offending a great many women, you are also excluding two larger groups of often vulnerable women and girls in order to include a smaller group. Which makes a mockery of any equality and diversity policy.
"People who menstruate" also implies there's something wrong with using the entirely accurate words "women" and "girls" when talking about who menstruates. And there is too much shame attached to too many of our experiences to allow this to happen.
These words are sex designators, that is they name the female sex and do so in two age categories - adult and juvenile. They do not stand in as designators for sex stereotypes or sex role stereotypes.
So we have precise, succinct and easy words to name our sex. Let's encourage everyone to use them.