My brother asked me to show him linux (I've been using it as my main OS for about 2 years). But I'm not the best teacher so I told him that he should learn linux by using it. The problem is, I'm not sure what distro I should show him, something that could actually teach him something, but not overly complicate the process, I've been using Arch and the beginners documentation isn't very easy to understand if you don't a lot about linux. I've thought about something like Ubuntu or Debian, but you could easily just use the environment and never learn anything about the terminal or system.
Nor do I really want him to join the /g/ hive mind of Gentoo and Sabayon.
Ubuntu/Mint, Opensuse and Fedora are all good places to start. Actually have a work purpose to learning those three since you can see those in enterprise. And all three are very well documented.
Sabayon and Manjaro are both fun and not hard to learn.
I can still learn a lot on my mint system mint 17.2 what I would suggest would be install a stable dirstro like linux mint or Ubuntu as the main os then use virtual box for the learning side. Have him install different distros and try to get them up and running then if he ever gets frustrated he can still have a usable OS.
I would say Mint but that is only because that is the only Linux OS I have used for the past 8+ months and have no experience with any other distributors. That being said, it still is very user friendly as a daily driver but you can actually get to the meat of things if you want (which is what I am doing right now).
I'd say give him something user friendly like a Debian distro and once he is comfortable learning the inner workings of Linux, then he can go and try out different distros like OpenSUSE, Elementary/Peppermint, Fedora, Slack, etc and see what he will really like.
If he used windows before: Mint Cinnamon (or almost anything Cinnamon), Kubuntu (Or almost anything KDE), Xubuntu (Or anything XFCE), Ubuntu Mate
If he used Mac before: Elementary OS, Fedora/Ubuntu Gnome (or almost anything Gnome 3), Ubuntu (unity), XFCE or Mate with Cairo or another dock.
If he has no inborn preference, and wants to use something that is intuitive without fitting specifically into one paradigm: Gnome 3, or perhaps Awesome or i3
Arch is great because it throws you in the deep and and forces you to actually learn to use whats great about linux instead of using your pc to browse the internet with firefox and nothing else. you could build your own OS to do that, or use a chromebook. Or even iOS. ;')
Apart from that, I give him a project to do. Give him a Ubuntu Server distro and make him set up a web server, email server, anything easy. Then let him touch gui.
It really depends on your brother's personality and what he want's to get out of it, right? But, before reading the other comments I'd recommend Manjaro.
1) Its close enough to Arch that you will be able to coach him when he needs it.
2) In most cases the Arch wiki, and to a limited extent even the forum are relevant and helpful. (Obviously If he were using Manjaro It would be best to direct questions to the Manjaro forums and not the Arch ones.)
3) The Manjaro community seems to have a more tolerant, and welcoming vibe.
4) It comes with a GUI installed. In fact its pretty much a usable system out of the box.
5) I have found that programs from the Manjaro repos, don't require as much reconfiguration as programs from Arch repos seem to need.
6) He'll still have access to the AUR.
As far as "not being the best teacher" goes, there are plenty of free online tutorials. This one is provided by the Linux foundation and eDX. Its a good broad stroke that cover's Linux/Unix fundamentals over multiple distros.