Well obviously these items are deeply offensive to women.
Firstly - if women are experiencing depression or mood disorders for whatever reason and want those around them to know - they can tell them (y'know what with us being sentient adult beings and all that...). One would hope they would be treated with sympathy and support.
On a larger scale though - for centuries women have been told that their femininity renders them inferior. We've been assigned everything from "the vapors" and "consumption" to the insistence that we have "feeble minds" and claims that periods render us everything from "unclean" to "incapable of making sushi"(seriously - this is why in Japan sushi chefs are almost all male!).
All of these theories have emerged to be completely false and the notion that women are less capable of managing their emotions during certain times of the month seem likely to hold just as little water. Note that these wristbands have not actually been invented - because a wristband absolutely 100% could never tell what stage a woman's menstrual cycle is at. The suggestion by the company that has raised the idea is that it would respond to subtle temperature changes but fertility testing kits which work based on body temperature take that temperature orally or rectally so you would literally have to stuff your wristband up your arse!!
Instead this story just serves to continue to promote the idea that women's menstrual cycles are the source of some problem and that men need "warning" about the stage of the cycle a woman is in (not mentioning that she may be pre-pubescent, post-menopausal, pregnant, suffering amenorrhea, trans-gendered or for any number of medical reasons, not having periods). Two women a week are murdered in this country by their male partners. Perhaps men should wear wristbands that read "I'm a man, I might attack you"...**
*Yeah, like fuck, we all know I have a Mooncup right?
**Hey trolls - why not quote this sentence out of context and then claim I hate men? Wouldn't that be fun? Try to spend all week doing it so you'll not be bothering me!