Debian provides it's own steam package.

https://packages.debian.org/search?keywords=steam
https://wiki.debian.org/Steam

It gives same error.

You can either drill down the dependency list trying to find out why "it is not going to be installed," with apt-get install or apt-get policy or ensure your sources are right. Are you sure you have multiarch enabled?

Yes , I'm sure to multiarch enabled (https://wiki.debian.org/Multiarch/HOWTO)

dpkg --print-architecture

amd64

dpkg --print-foreign-architectures

i386

cat /etc/apt/source.list

deb [arch=amd64,i386] http://ftp.tr.debian.org/debian/ jessie main
deb-src http://ftp.tr.debian.org/debian/ jessie main

deb [arch=amd64,i386] http://security.debian.org/ jessie/updates main
deb-src http://security.debian.org/ jessie/updates main

# jessie-updates, previously known as 'volatile'
deb [arch=amd64,i386] http://ftp.tr.debian.org/debian/ jessie-updates main
deb-src http://ftp.tr.debian.org/debian/ jessie-updates main

deb [arch=amd64,i386] http://httpredir.debian.org/debian jessie-backports main contrib non-free
deb [arch=amd64,i386] ftp://ftp.debian.org/debian stable main contrib non-free

apt-get install steam

Reading package lists... Done
Building dependency tree       
Reading state information... Done
Some packages could not be installed. This may mean that you have
requested an impossible situation or if you are using the unstable
distribution that some required packages have not yet been created
or been moved out of Incoming.
The following information may help to resolve the situation:

The following packages have unmet dependencies:
 steam:i386 : Depends: libgl1-mesa-dri:i386 but it is not going to be installed
              Depends: libgl1-mesa-glx:i386 but it is not going to be installed
E: Unable to correct problems, you have held broken packages.

libgl1-mesa-dri:i386 : Depends: libdrm-intel1:i386 (>= 2.4.48) but it is not going to be installed
                        Depends: libdrm-nouveau2:i386 (>= 2.4.38) but it is not going to be installed
                        Depends: libdrm-radeon1:i386 (>= 2.4.31) but it is not going to be installed
                        Depends: libdrm2:i386 (>= 2.4.38) but it is not going to be installed
                        Depends: libllvm3.5:i386 but it is not going to be installed

If you try to install those packages by yourself, why can't they be installed?

They can be installed buy steam gives same error.
I downloaded from https://packages.debian.org/jessie/i386/libgl1-mesa-glx and copied to current directories.

steam

Package libgl1-mesa-dri:i386 needs to be installed
Package libgl1-mesa-glx:i386 needs to be installed
Package libc6:i386 needs to be installed
Running Steam on debian 8 64-bit
STEAM_RUNTIME is enabled automatically
Error: You are missing the following 32-bit libraries, and Steam may not run:
libglapi.so.0
libxshmfence.so.1
libdrm.so.2
Installing breakpad exception handler for appid(steam)/version(1476379980)
Installing breakpad exception handler for appid(steam)/version(1476379980)
Installing breakpad exception handler for appid(steam)/version(1476379980)
Installing breakpad exception handler for appid(steam)/version(1476379980)
[2016-11-20 00:05:26] Startup - updater built Oct 13 2016 00:47:16
Looks like steam didn't shutdown cleanly, scheduling immediate update check
[2016-11-20 00:05:26] Checking for update on startup
[2016-11-20 00:05:26] Checking for available updates...
[2016-11-20 00:05:27] Download skipped: /client/steam_client_ubuntu12 version 1476379980, installed version 1476379980
[2016-11-20 00:05:27] Nothing to do
[2016-11-20 00:05:27] Verifying installation...
[2016-11-20 00:05:27] Performing checksum verification of executable files
[2016-11-20 00:05:27] Verification complete
[2016-11-20 00:05:28] Shutdown

@EmreOvunc, just so it's clear. Steam is trying to tell you you do not have a sane 32 bit opengl implementation installed. You need to add that to your system in order to use steam.

@Tele42 I already installed 32-bit library by using "dpkg --add-architecture i386".
Last week, I was using steam with my Ubuntu, but I change my operating system to Debian and it does not work now.

Hey! Come look at this reddit thread about installing steam on Linux, because you may have missed a step that's been written:

https://www.reddit.com/r/GlobalOffensiveLinux/comments/5cmogn/csgo_tweaks_sticky/d9y0iym/

Finally, I solved this problem and I tried almost everything to install steam on the internet.
It's just about libdrm-intel1 library.
Solution that error for debian users is:

The following packages have unmet dependencies:
 steam:i386 : Depends: libgl1-mesa-dri:i386 but it is not going to be installed
              Depends: libgl1-mesa-glx:i386 but it is not going to be installed
E: Unable to correct problems, you have held broken packages.

1. Open "Synaptic Package Manager"
2. Search "libdrm-intel1
3. Right click to downgrade its version to stable one.
4. Then run steam from the command line.
5. Steam wants to install missing packages& libraries, press "Y" to install them.

I think that some packages or libraries use non-stable version and that causes some installation error like Steam.
Thanks for advices.

I recently face the same issue.

Package libgl1-mesa-dri:i386 needs to be installed
Running Steam on debian 9 64-bit
STEAM_RUNTIME is enabled automatically
Installing breakpad exception handler for appid(steam)/version(1496897923)
libGL error: unable to load driver: i965_dri.so
libGL error: driver pointer missing

Then, I try to install
sudo apt-get install libgl1-mesa-dri:i386
But It failed

The following packages have unmet dependencies:
 libgl1-mesa-dri:i386 : Depends: libgcrypt20:i386 (>= 1.7.0) but it is not going to be installed
E: Unable to correct problems, you have held broken packages.

Then, I tried to install libgcrypt20:i386, but failed. I lose the error log. However, If can't install libgcrypt20:i386 like me. It likely to be the same issue.

Solution
I manually download libgcrypt20 (1.7.8-2) both amd64 and i368 (multiarch) from https://packages.debian.org/sid/libgcrypt20

1. Install the deb files (amd64 and i386) using dpkg.
2. sudo apt-get install -f
3. sudo apt-get install libgl1-mesa-dri:i386

Now, it works, I can install libgl1-mesa-dri:i386 on my Debian Stretch recently updated from Jessie
Then I can run the installed steam that I downloaded from steam official website.

I installed Steam on Kubuntu 16.04 LTS using the command line and get the same error when I try to start it.

When I run the installed binary from the menu it tells me:
you are missing the following 32-bit libraries libgl.so.1

Why are you not compiling Steam in 64 bit? Zero/Zilch/Nada gamers use 32 bit Raspberry PIs. I'm pretty sure you can compile all OSes with appropriate libraries using Gitian to easily create 32 and 64 bit binaries

I'm using NVIDIA version 384 drivers for gtx 1070.