Hello,
Sorry, I went too fast on your question.
The default value of the product categories can be override via the template system but it can't be emptied.
When you create a new product, the current browsing category is used has the product category.
So, because you were in the category "product category" in your product listing, when you click on "New", that same category is used. You ask to create a new product where you were.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.