It seems to trigger based on the browser window being too small. Yes, it is possible to access messages by requesting the desktop site, but it's pretty inconvenient.
I'm not sure messaging can work well in a mobile browser because notifications would not be timely, but maybe you're using it for a purpose that doesn't require instant notifications.
>maybe you're using it for a purpose that doesn't require instant notifications.
Yeah, generally if I'm messaging in Facebook, it's someone I don't know well - often kind of temporary connection through a community group, like arranging a time to exchange a second hand thing. I'm happy to manually check when needed. (That is, back when I used to use this method before I gave up and got the app.)
This comment does give a bit of insight into why Facebook tries to prevent people using mobile browsers for messaging though.
