“tlmgr update --self/all” won't work even after a fresh installation of Texlive 2016 [closed]

Question

I was unable to update Texlive 2015 using tlmgr so I installed the latest version, that is 2016 following the instructions. After the installation of 2016 I removed the old (2015) version and set the path to

PATH=/usr/local/texlive/2016/bin/x86_64-linux:$PATH

I also compiled a lot of tex files without any errors and also the installation log file (of 2016) showed no signs of errors. Then I tried to check if the update command (tlmgr update --self ) works, it didn't ! The error message was:

All good.
Uncompressing TeX Live Manager Updater............................................................................................................................................................................
./runme.sh: Cannot find TeX Live root using kpsewhich --var-value=SELFAUTOPARENT.
./runme.sh: Please set your PATH as needed, otherwise it's hopeless.

Can anyone please help me understand what needs to be done, for example: I don't understand why is it still asking for a "PATH" given the fact that I have already set it up typing the following line in the terminal:

PATH=/usr/local/texlive/2016/bin/x86_64-linux:$PATH

Out of curiosity I then repeated the update command by specifying the whole path, that is:

/usr/local/texlive/2016/bin/x86_64-linux/tlmgr update --self  

And it worked, because the output was:

tlmgr: package repository http://ctan.mirror.garr.it/mirrors/CTAN/systems/texlive/tlnet (verified)
tlmgr: saving backups to /usr/local/texlive/2016/tlpkg/backups
tlmgr: no self-updates for tlmgr available.

So I tried to update the packages instead by using:

/usr/local/texlive/2016/bin/x86_64-linux/tlmgr update --all

which also worked and returned:

tlmgr: package repository http://ctan.mirror.garr.it/mirrors/CTAN/systems/texlive/tlnet 
(verified)
tlmgr: saving backups to /usr/local/texlive/2016/tlpkg/backups
[ 1/20, ??:??/??:??] update: europasscv [378k] (41201 -> 41866) ... done
[ 2/20, 00:05/04:04] update: glossaries-extra [3355k] (41486 -> 41856) ... done
[ 3/20, 00:09/00:44] update: latexpand [8k] (37592 -> 41873) ... done
[ 4/20, 00:10/00:49] update: markdown [333k] (41376 -> 41855) ... done
[ 5/20, 00:12/00:54] update: mweights [3k] (31268 -> 41867) ... done
[ 6/20, 00:16/01:12] update: newpx [1707k] (39698 -> 41863) ... done
[ 7/20, 00:22/01:10] update: newtx [4028k] (40165 -> 41864) ... done
[ 8/20, 00:27/00:50] update: parnotes [129k] (41775 -> 41868) ... done
[ 9/20, 00:29/00:53] update: texlive-docindex [220k] (41843 -> 41862) ... done
[10/20, 00:31/00:56] update: udesoftec [618k] (40613 -> 41872) ... done
[11/20, 00:32/00:54] auto-install: cormorantgaramond (41865) [5284k] ... done
[12/20, 00:37/00:42] auto-install: phffullpagefigure (41857) [250k] ... done
[13/20, 00:38/00:42] auto-install: phfnote (41858) [667k] ... done
[14/20, 00:39/00:42] auto-install: phfparen (41859) [311k] ... done
[15/20, 00:40/00:42] auto-install: phfqit (41860) [343k] ... done
[16/20, 00:40/00:41] auto-install: phfquotetext (41869) [201k] ... done
[17/20, 00:41/00:42] auto-install: phfsvnwatermark (41870) [208k] ... done
[18/20, 00:42/00:42] auto-install: phfthm (41871) [397k] ... done
[19/20, 00:43/00:43] update: collection-fontsextra [2k] (41736 -> 41865) ... done
[20/20, 00:44/00:44] update: collection-latexextra [6k] (41853 -> 41871) ... done
tlmgr: package log updated: /usr/local/texlive/2016/texmf-var/web2c/tlmgr.log
running mktexlsr ...
done running mktexlsr.
running mtxrun --generate ...
done running mtxrun --generate.
running updmap-sys ...
done running updmap-sys.

I would like to know how can I really solve this "PATH" problem. I can specify the whole path each time but I really don't want to.

Some other information that I would like to provide are:

which tex

returns /usr/bin/tex

Similarly which latex and which pdflatex etc return /usr/bin/latex and /usr/bin/pdflatex

So clearly the path specification didn't work!

---

Forgot to add the log file of a tex compilation which I think is important

The log file was too big so I decided to save it as a "google do" and provide the link here.
I am pasting the first line though:

This is pdfTeX, Version 3.14159265-2.6-1.40.16 (TeX Live 2015/Debian) (preloaded format=pdflatex 2016.5.23)

Does it say I am still using texlive 2015? I don't know how is that even possible because I have erased the whole directory /usr/local/texlive/2015 there's only one directory/file inside /usr/local/texlive and that is 2016.