Why Open Source?
1. Cheaper. It is cost effective. With open source operating systems and software, you have full control over cost. It is up to you use completely free Ubuntu, Centos, openSUSE or non-free like Red Hat and SUSE Enterprise Linux versions or mixture of both.
2. Upgrade-ability. If free Linux system runs out of support you just upgrade for free again.
3. Security. Open source systems are more secure in good hands because of multiple reasons:
Because the source code is open they can not even think about fitting back-doors or secret functions there hoping nobody finds out like proprietary programmers constantly do.
Vulnerabilities found and fixed by community usually faster than hackers find them because the code is open. It is exactly opposite with proprietary software.
Different approach. Some things considered normal on proprietary software are unthinkable on Linux. You can not have a user without password. You cannot install software without entering a user with administrator rights password even if you are already logged as that user.
Dependencies (like .dll files in Windows) not installed with software packages, but for the majority of software from official repositories.
Linux does exactly what supposed to do. If it is a server it usually without Graphical User Interface and without any unnecessary features.
4. Performance. For the same reason, performance is better and requires lesser system resources. And It does not have to check constantly if the system really licensed or whatever ever extra propriety systems continuously do.
5. Flexibility. You can take HDD from 5 years old computer, plug into completely different new one and it will start and work without any restarts, reboots and blue-screens.
Where Open Source?
Regarding w3techs statistics, 84% of web servers are based on Apache and Nginx open source software. Therefore methodologies they use do not count subdomains. It means that all traffic to WordPress.com subdomains (126M unique visitors per month) they count as one. The same thing with Blogger.com and free subdomains.
There were studies with including revenue in market share comparison. Keeping in mind the fact that Linux cost nothing these studies could not hold any criticism and today are deleted from servers, but old posts like Quora 2013 still can be found where people talking 47.9% of the servers worldwide ran Windows Server whereas 40.5% ran Linux.
Closest to the truth looks W3Cook’s in May 2015 made an estimation of 98.3% Unix-like and 1.7% Microsoft Windows WWW servers.
This very site you are reading runs on Linux Apache web server.
Android.