There can be any number of issues.
First, your logo may infringe on somebody else's work. If it even says Minecraft, for example, you're running into issues with Microsoft. If it's too similar to what somebody else has done, it can be infringing itself.
Also, it's automatically copyright protected as soon as you create it. It's very rare than creators fully transfer copyright, and say others can do whatever they want with their work. Usually, a creator gives another person permission to use their work. That's called a license. It's usually pretty specific about the kinds of things that are okay, and are not okay.
If he starts using your logo with permission, he can run into problems. Let's say two years from now, his server has become super popular, and people love the logo. Now they want to use it as computer wallpaper, and they want t-shirts with it, etc. You probably didn't intend to give him permission to do that when you let him use the logo for his server. Even if you thought of it, you thought it would be common sense that he'd talk to you about it if something like that ever happened. Well, was your logo really "free" or not? What if Microsoft wants to buy his server, including the logo, for $10 million. Is he allowed to sell it along like that? What if McDonald's wants to do a promo with your logo, and they promise they'll give you "credit," and slap your name on Big Macs for a month? Do you want to have something to say about that?
Anyway, he can indeed have copyright issues, both with you infringing others, and with licensing with you. Your work is copyrighted automatically. And unless you're fully transferring copyright to him, and know what you're getting into, it's not worth his hassle.