So just to be sure are you using a commercial account, so say an Outlook.com or a Gmail.com for your personal account sign in?
However and more likely for me is that the email address being utilised effectively as your username is associated with a domain that already has Teams? This can happen if say for my outlook.com account I setup an alias of my firstname.lastname@example.org.
Although the more I think about this but still leaving in the above in case it is of use. Is that if you truly signed up for a Personal Teams account as in Family and Friends then to you can only interact with it via the mobile app.
Or did you mean the free version of Teams?
So for me there are effectively 3 types of Teams Orgs at the moment:
1. Corp by way of an M365 plan 2. Free slimline version 3. Personal family and friends