Android doesn't allow you to install an older version of an app over a new version. F-Droid has the UI for it but it doesn't work, the security policy prevents the install.

There's probably a good reasons for that, but I can't think of it other than the flawed reasoning of "it can't be a good idea to roll back an update". I'm sure even Google can imagine a situation where, say, an app update got infected with malware or something like that and it's in everyone's best interest to roll back to the previous version until a clean update arrives. Preventing rollback means the only way to do that is for the user to manually uninstall the app and reinstall the desired version.

Okay, I can think of a possible reason for that policy: it prevents malware from downgrading a target app to a former (official, signed) version which can be exploited. I don't know how realistic this scenario is, though.