Maybe “should” is too strong a word. I am thinking that title could be more like “why would you want to blog”. Blogging is really a personal choice. It is another social media tool, much like Facebook, Twitter and Instagram are. The advantage of blogging over those social media networks though is that you get total control not only of your content, but also of your subscriber list.
Even if you have 10,000 “likes” or “fans” on Facebook, you still have to PAY every single time you want to communicate with them now even though you probably paid for advertising to get those fans to begin with. Sounds crazy, and it is, but it is what it is. When you have a subscriber list via your blog, you can email those folks anytime you wish to without having to pay an extra dime for that email. In fact, some business pages will encourage their fans to become subscribers so they don't miss any updates because you just never know with Facebook who is seeing your feed or not, EVEN when you pay for your fans to see it. This is simply because you just don't know how many other fan pages are competing for your subscriber's eyes on the feed.
Here is another reason to have a blog and build your list via that blog, it will help brand your business! You content is more personal, your community is tighter, you can control what they see and when they see it, and you can promote other activities at the same time. A blog will help solidify your brand and customer loyalty and help you deliver a consistent look and feel (unless you change it).
Many bloggers tie their blogging activity to their Facebook feed as well as their Twitter feeds so everything is seamless for your viewer. But driving people from your Facebook page to your blog and encouraging the subscription will really, really, really be a lot more productive for your business than counting on all those likes to deliver return visits!
And last but not least, you blog so you can help you find other folks who also love the same things you do or folks you can inspire with your knowledge or guidance. Blogging will help you connect with others purely based on the content you share. If you are wondering if blogging is for you, head over to WordPress.com and start with a free blog first and see how you like it.