[Galaxy Tab 2 Q&A, Help & Troubleshooting] spectrum33:
Well I had the exact same problem, and I think that the SuperSU included on the CF-Auto-Root file is outdated or something.

I was on android 4.2.2 but I have the Galaxy Tab 2 10.1 P5110.

I searched the forums and came up with a solution for our problem. I think that SuperSU is outdated on that CF-Auto-Root file or it was the custom recovery that it installs thats outdated or messed up for android 4.2.2, because right after it does its thing, we get the tablet default recovery again.

Since I dont know how to make a new CF-Auto-Root file, I tried to install an updated custom recovery through Odin3 instead of the CF-Auto-Root file, and it worked. Then I entered on the TWRP recovery and installed an updated SuperSU, restarted the tablet, and it worked too. I had now a rooted tablet with a permanent custom recovery, So i followed to install a custom rom, etc.

So now the steps I did:

(I am not responsible if it doesnt work for your tablet and messes something up or brick it, so please follow on your own risk, or maybe wait for some expert on this things to say if its safe or not. All i know is that it worked for me.)

Step 1: Download Stuff

Download and install samsung usb drivers

Go to Samsung website and search for your device. Go to downloads and download the USB Driver and install it.

Download Odin3 1.85_3

Go to this topic and download Odin3 3.85_3 from the "What you need:" section. Extract it on your computer.

Download TWRP recovery

Go to TWRP website, click "Get TWRP for your device", search for 5110 (doesn't have the 5113 version, and I think that the 5110 is the same and works too), scroll down to "Download - Odin Flashable Tar:" and click the "5110 only" version. It will open another page, scroll down for the most recent version and download the .tar file. Extract it on your computer.

Download SuperSU for TWRP

Go to Chainfire website and download that SuperSU version for TWRP. Dont extract, just put it on your SD card for the tablet.

Step 2: Doing stuff.

Install samsung drivers, extract Odin to your computer and put the SuperSU file on your SD card for the tablet.

(To avoid confusion about using the Volume rocker switch, I'll refer to side closest to POWER button as LEFT/Volume DOWN and side away from power switch as RIGHT/VolumeUP. )

1: Turn off the tablet and restart it on download mode. To enter download mode, press Power Button + Volume Right. When the warning appears press Volume Left to enter download mode.

2: Now open Odin3 1.85, click PDA, select the TWRP .tar file you downloaded.

3: Make sure to uncheck the "Auto Reboot" option. The only checked thing must be "F. Reset Time".

4: Connect usb cable to tablet. Press start. When it finishes, the box will turn green and says "pass!" you can remove the cable.

5: Now press Power button + Volume Left. Keep pressing it, the tablet should restart and when the samsung galaxy tab 2 screen appears, let go of the power button, but keep pressing Volume Left until the TWRP recovery screen appears.

6: Now inside TWRP recovery menu, press Install. On the top part of the screen press Storage and and change to external storage or SD card. Now select the SuperSU file and install it by swiping that thing. After it install and says successful, press reboot.

Congratulations ! Now you have successfully rooted your tablet and you have a permanent custom recovery ! You can now install a custom rom, etc.

Some notes:

I used TWRP recovery because i used it on my smartphone. So thats what I learned to use, so I used it on the tablet too. Feel free to use other custom recovery and adapt the tutorial for it.

It worked for me. If it doesn't work for you, or something is failing on some step, try to read everything again and re-do.

Credits:

* I based this on this topic and its replys (the last comment on this page.)

* Also credits for the Odin3 creator, SuperSU creator and TWRP team.

I just put together things from here and there, but without this persons, creators and stuff, we would not be able to make this happen.