I positively and absolutely agree about the importance of owning your own site.
1.
Control. You can control the layout, the type of content, the functionality... all of it. If you're able to design the site yourself, fine - but for business purposes get a professional site designer. Make sure though that YOU, the owner, have full access to the website's innards. Don't be at the mercy of a company who won't allow you cPanel access, for instance.
2.
Security. You have all heard of the disturbing breaches in security which saw very personal details made public on Facebook accounts. If your "site" or web presence is on those sorts of accounts (Twitter, Facebook, WordPress, MySpace, MyWhatever), you cannot prevent such security breaches because it's beyond your control.
3.
No Sudden Chop. You won't find your "site" or account suddenly suspended. Have your own website, and as long as your server is fine, your site is up and good to go. If something does happen to your server, you'll at least have your website files saved so you can upload again onto another server/host. And if you have regular backups, any new content will also be saved because you can upload the latest backup as well.
4.
A more professional look. There's no doubt that a website URL such as
www.mybusinessnamewebsite.com.au or something like that is more professional-looking and inspires more confidence from potential customers than a website URL which is clearly a subdomain of a free provider or an account on social media.
5.
Drive the traffic to YOUR site. Those who depend on Facebook or Twitter or whatever are really using the social media website to bring customers to them. Thus immediately come the following points:
i. Non-Facebook users are less likely to find you than Facebook users - immediately limiting your potential customers;
ii. If Facebook goes down, so do you;
iii. If Facebook dies out, so does your site;
iv. If ANYTHING happens to Facebook, you'll have lost your customer base by and large, and when you start up again elsewhere (FaceTwitter, MyNewBook, whatever), you'll have to build up followers in THAT NEW MEDIA. BUT... if you use social media to drive traffic to YOUR SITE (not your Facebook "site", or whatever) - as ONE of your methods of attracting business, you'll gain customers who will find you through your WEBSITE - and means Facebook could perish without taking you with it.
6.
Your content is your content. Did you know that when you post something onto a website or a blog, where you are no the owner, that content or intellectual property can no longer be regarded as your own? You cannot demand the site remove your content if you decide to leave. You cannot demand the site restore your content if they remove it. You cannot - in fact - demand anything. This is crucial for people who deal in words or images. Do NOT trust other websites with material over which you want and deserve copyright or ownership or control. Of course, other people may COPY your content once it's online, even if it's on your own website, but there are many incidences of people who have received a C&D letter from solicitors acting for clients whose copyrighted material has been used without permission. The bottom line: you CAN take action against copyright breachers if you have your own content on your own site marked as copyright, but you haven't a hope if you post that content on social media websites.
In short - your own website is a very, very good idea. Of course you'll be responsible for the design and functionality (or you'll hire someone to be), so it's more work initially, and of course you'll be responsible for regular backups - but it is worth it on every level.