I found the answer. The main problem is:
First of all woocommerce plugin has own ID system. And wordpress has own ID system. And it happened that with the same ID was two different items. For example:
Woocommerce category name “my category” has ID: 13
And
WordPress page “Logout” has ID: 13
So, in woocommerce where is function called “woocommerce_nav_menu_items” is checking pages like “Logout”, “Change password”, “View order”, “Edit address” to avoid show if user is not logged in. And this function is checking if you are not logged in, unset all these pages which would be in menu.
And it’s happened what my created category in woocommerce was with the same ID like created page “Logout”.
My suggestion:
If this will happen to you just delete created category and create a new one, because the system will assign another ID to your category.
I hope this will help for many people.