Owning a national trademark — for example, a US trademark — does not automatically lead to worldwide trademark protection against copycats. This is why, for example, Highsnobiety parent company, Titel Media owns separate “Highsnobiety” trademarks in the US and EU.
According to the so-called “territoriality principle,” a logo only enjoys protection as a trademark where it is registered as a trademark — for a national German registration with the [German Patent and Trademark Office] DPMA, EU-wide with EUIPO, etc.
This application is facing two significant obstacles. Firstly, there might have been earlier trademarks in Europe registered by Supreme Italia. Secondly, the EUIPO might find the “Supreme” logo is lacking any distinctive characteristics and thus cannot be protected as a trademark at all.