I agree that having a website and not relying fully on social media is good (having full control over how your content is presented, not having to worry that you'll lose your audience completely if a website goes down or falls out of favour or changes in a way you disapprove of, having a nice neat memorable "runewriters.com" URL to tell people rather than "tapas.io/series/runewriters"),
but I don't agree that you should have your own website instead of having social media. Social media is still important! How on earth are people going to find you? Like, I guess you can make contacts at conventions and stuff, maybe do some really thoughtfully placed paid advertising? But if you're not hanging out where people are then it's going to be a lot harder to tell people about your work, and it's going to take way longer to grow your audience.
I do both! My comic is on its own website, but I still participate pretty regularly on twitter and tumblr. I don't agree that it's impossible to grow on these platforms unless you're already big -- we all start somewhere -- it's just going to take time and participating rather than just self-promotion in order to grow your audience.