Show  on user page if user page belongs to current user
To do this right you will need to use this combination of tests.

Is the user logged in {% if logged_in %} ?

Does the user have the permission needed to edit their profile with {% if user.hasPermission('depends on your site setup') %}?

Is the owner of the node the same as the current user?  {% if node.ownerId  == user.id %}

NOTE: The snippets above are not tested.  You may have to tweak to get the correct info (e.g. getOwnerId SHOULD equal node.ownerId.. but twig may have a different opinion).