An account on social media is like couch-surfing. It's not really "your" space, but you can tell people to send you mail there. It's not your house either, and so you don't have to pay for it, but you have to be a good guest and watch a lot of ads. The owners of the house watch you all the time, and the longer you stay on the couch the more information they have about you.
Social media has other ugly side effects, and other ways it is bad on a less individual level, but in terms of a public interface these are the simplest drawbacks.
Customizing a website from a is like renting a house from a large company. You can't put holes in the walls, and sometimes the rent goes up suddenly. You'll have to rely on your domain name to get exposure to an audience that is relevant to what you have on your page.
If someone looks up "horse blog", and you run a horse blog at horseblog.com you might be the top of the search result page, but you'll be paying a web hosting service a monthly fee in order to have an audience directed to your page and not to horse.com, a purveyor of horse supplies.
Acredited domains with relevant domain names might be more expensive and harder to acquire. Websites with those more expensive, more relevant domain names might get more traction in a search engine’s algorithm, and so they get that much more exposure.
Like this website. Hosting a website like this is like buying an empty plot of land for zero dollars and zero cents. There are lots of very knowledgable and helpful resources near your empty plot of land, and they are accesible for free too. The only barrier here is time constraint and relative exposure. If your website is about something very obscure, maybe you'll land at the top of a page of search result page. More likely, you'll have to rely on other internet surfers to find and link your page to theirs. Their audiences will find you that way, and they won't pay a penny to do so. This website is hosted on Neocities.