Reduce amount of logic in your templating: set business in your array definition, not in template body.

gistfile1.twig

<ul class="nav navbar-nav">
    {% set navbar_active = navbar_active|default(null) %}
    {% set navbar_menu = navbar_menu|default([
        {
            'show':   app.user and is_granted('ROLE_ADMIN'),
            'active': navbar_active == 'design',
            'label': 'Design',
            'href':   path('admin_design'),
        },
        {
            'show': app.user and is_granted('ROLE_ADMIN'),
            'active': navbar_active == 'administration',
            'label': 'Administration',
            'href': path('adminuser_list')
        },
    ]) %}
    {% for menu in navbar_menu %}
        {% if menu.show|default(true) %}
            <li{% if menu.active|default(false) %} class="active"{% endif %}>
                <a href="{{ menu.href }}">{{ menu.label }}</a>
            </li>
        {% endif %}
    {% endfor %}
</ul>

menu.show|default(true) will not do what you expect, because a false value will give you the default, so the item will always be shown