Hi mircea82,
We appreciate you reaching out for help managing conference calls on your iPhone. Let's get to the bottom of this together.
To start, please tell us more about what's going on, so that we're on the same page.
Have you noticed if this same behavior occurs on every conference call, or only when calling certain contacts? What happens if you follow the steps in this guide under step 2 of the section titled, "Start a conference call" to make a call private and swap between calls?
While on a call on iPhone - Apple Support
It's important to note that if you've got a CDMA carrier, there isn't an option to switch between calls if the second call was outgoing. Also, if you end the second or merged call, both calls are terminated. You'll want to reach out to your carrier if you have any questions about whether they utilize a CDMA or GSM network.
Have a great day!