How do I remove one person from a group in my iPhone contact’s?

For messages, you can only remove someone if the group has four or more people, and everyone is using an Apple device, like an iPhone, iPad, or iPod touch. For more info, see:

Add and remove people in group text messages on your iPhone, iPad, or iPod touch - Apple Support

you need to do it from a computer. You cannot do it from the iPhone. on the Mac open contacts>select the group>select the person>swipe left>tap delete.