The default is set based on the View XML:

https://github.com/odoo/odoo/blob/13.0/odoo/addons/base/views/res_partner_views.xml#L291

context="{'default_parent_id': active_id, 'default_street': street, 'default_street2': street2, 
          'default_city': city, 'default_state_id': state_id, 'default_zip': zip, 
          'default_country_id': country_id, 'default_lang': lang, 'default_user_id': user_id, 
          'default_type': 'other'}">

The context contains all the default values that are "sent" to the popup form.

You can override these values with your own View:

If you hover over the radio buttons in Developer Mode, you can see the value you need to have instead of OTHER in order to default to CONTACT.

Then make a View like this:

<field name="child_ids" position="attributes">
  <attribute name="context">{'default_parent_id': active_id, 
        'default_street': street, 'default_street2': street2, 
        'default_city': city, 'default_state_id': state_id, 'default_zip': zip, 
        'default_country_id': country_id, 'default_lang': lang, 'default_user_id': user_id, 
        'default_type': 'contact'}
  </attribute>
</field>