Not doing it wrong. And depends on what you are trying to do.
What you are doing is allowing the other person full access to the calendar, so, can see why they make one login to iCloud. And this only will work with other iOS users.
If just wanting to give a person a read-only view to your calendar:
In Calendars, tap "Calendars"
Tap circle-i next to Calendar you want to share
Scroll down and make the calendar public
You now have a "Share" option below that where you can get the URL to the calendar and mail/message to the other person. As long as they use an app that speaks CalDAV (most everything these days does), no iCloud sign-on required.