There are many reasons to own your own website, but let's focus on five:
You should own your own narrative.
I don't think I need to tell you how beneficial the internet can be. I also don't need to tell you how potentially dangerous it can be.
Even if your website is super simple and has not much more than your name, a short bio, and a contact form, it's still worth having so you can own your story and make sure no one tells it inaccurately.
Make potential clients' life easier.
If someone wants to work with you, even if it's just a thought right now, give them the possibility to learn more about you without the need to do extensive research.
If you make someone work hard to learn about your business, chances are they will give up at some point. Having your own website gives potential clients the opportunity to quickly and easily learn about you and your offering.
You can even use your website to offer clients some references by including testimonials on the site. The bottom line is, you should have a site so people don't have to work too hard to learn about you.
Not being visible when people search for you is kind of a red flag.
I always compare this to growing up and finding out that a kid in my class doesn't have a TV at home, or today, finding out that a person doesn't have internet at home.
I don't know about you, but that is a red flag to me. I know I am slightly over-simplifying and I realize that in some cultures people don't have a TV or internet access, but if you work in the business sector, not having your own website is kind of the same thing. It makes people ask themselves, "Why doesn't this person have a website? Who doesn't have a website today? Something must be up."
Prevent someone else from buying it and potentially causing you professional damage.
Here is a personal story. My website had expired a few years back and before I could renew it, I'm talking within a few minutes, someone else bought it with malicious intent. They even threatened me that they would put illegal content on the site so when someone Googles me, that's what they see.
Now, I realize that not everyone has to worry about something like that, but why take the chance? Just own your own website, and even if you leave it blank -- which you shouldn't -- at least no one else can own it.
The internet can be a dangerous place, and there are some evil people out there. Don't tempt them.
Give people an easy way to contact you.
Finally, why make people search for you when they want to reach out? Obviously, if the message the person wants to send is more of a personal thing, they can reach out on social media, but if it is more business-related in nature, you want to give them an easy way to reach out.
The first thing a business acquaintance will do when trying to contact you is Google your name. If you own your own domain, your own website, that person doesn't have to search too much to be able to contact you.
You can also include a contact form, so the people who reach out share the exact information you need -- nothing less and nothing more. In other words, owning your own domain and building your own website makes everyone's life easier.
In conclusion, you should buy your-name-dot-com for various reasons, and if you don't know where to start, how to buy a domain, or how to build the site, find someone who does. It should not cost you too much to buy, unless your name is Bill Gates or Elon Musk.