iOS 13 has changed the way iPhone users rearrange their home screen icons and delete apps. Long-pressing on an app icon doesn’t work the same anymore.
It brings a contextual menu instead of putting the apps into the “jiggle” mode. Unless if you ignore the menu and keep pressing on the app, then they’ll start to jiggle.
It was confusing, even for tech-savvy people. Apple understood that and came up with a fix with iOS 13.2. Feel free to download it, but always remember to backup your iPhone first.
Apple makes it now easier and more intuitive to remove apps and rearrange your home screen. With iOS 13.2, if you long-press on an app icon, a contextual menu will pop up again, but with different options.
The options that appear on the popup menu will be specific to certain apps. But there will be two additional options that will remain the same regardless of what app you long-press on: Delete App and Edit Home Screen.

Tap “Delete App”, then confirm to remove an app from your iPhone. The Rearrange Apps option has been renamed as “Edit Home Screen”.
If you wish to rearrange your home screen, then tap on Edit Home Screen. Once the apps start jiggling you can move then around the screen.
If you wish to hold longer until the apps enter into the “jiggle mode”, then drag them around or tap on the X to delete them.
You can still do that. The update hasn’t removed this way, it only gives you the options right within the pop-up menu.