I know this is a necro thread but I thought I would chime in for those that need help since this comes up as the top on google search for "Read-Only ADB push".
If you're running into this:
1. Make sure you are rooted with SuperUser of some type installed
2. On your machine with adb installed, do the following:
[HIGH]
--# adb devices
(make sure your device shows up)
--# adb root
(this restarts the adb daemon as root on the phone)
--# adb push blah bleh
(this should now run without issue)
[/HIGH]
You DO NOT need to remount the /system symlink with rw permissions. A lot of people will do this and forget to remount it back to ro permissions.
After submitting 'adb root' I get: adbd cannot run as root in production builds