So, tell me why does a web site do this...for security reasons??
The feature is there for institutions like banks to disable password saving.
In this case, however, I suspect the following: In Internet Explorer on Windows, there is a special plug-in in the browser that handles login. I guess Microsoft thought this was the easiest way ti disable the password manager in Internet Explorer and leave the job to their plug-in. The other browser’s password managers are just collateral damage.