Microsoft 365 features that help users manage their subscriptions, account settings, and billing information.
Dear Suzanna,
The prompt you are seeing comes from the link itself rather than anything on your account. A personal booking page normally lets anyone book without a Microsoft account, attendees are offered the choice to sign in or continue as a guest. Since you are not being given that option, something is off with the link or how the page was set up on his side.
The most likely explanation is that he shared the wrong address. The page organizers use to create and edit their booking page does require a work or school account, because it is the management view rather than the public page. If he copied the address from his browser while editing his page, instead of using the share or copy link option, you would see exactly this prompt.
Before going back to him, try opening the link in an InPrivate or Incognito window without signing in to anything. If the page loads and lets you pick a time, it was simply your personal account already being signed in.
If the prompt persists, ask him to open his booking page and use the share or copy link option rather than pasting the address from his browser bar. Alternatively, he can simply send you a normal meeting invitation to your email address.
For reference: Personal Bookings FAQ
I hope this helps. Looking forward to your reply.
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