It is cool, and as a Native, I encourage you to explore those ties and reconnect with them. You are the product of people who transcended genocide, and that is something to be proud of. In regards to your statement, I am hoping I can shed some light on why some Natives react the way they do to "I'm part Cherokee" people.

For starters, I, and many of my Native friends, do not like the phrase "part" Native. We're just Native. I myself am mixed, and biologically am more European than Native, but I identify as Native because that is the lifestyle I practice and the community I am active in. Viewing our self in parts, or quantifying/measuring our identity was never something our ancestors did. Instead, it was a practice that was instilled by colonization. In trying to maintain our traditional way of life, we don't really view ourselves in parts. We're just Native.

This often means having to experience pretty severe social issues. I don't know how familiar you are with the state of some reservations, or the contemporary problems that are heavily concentrated in our demographic, but plainly speaking, it's hard to be Native American. So, when you fully identify as Native, even if you're mixed, that means opening yourself to hurt. When people say, "I'm part Cherokee," it often translates to: "I'm Native when it's cool, fun or easy to be." When you suffer, when your people suffer, and you have people who are only reaping the benefits of this identity, it's frustrating. Having Native blood is really cool, but only acknowledging it when it's convenient is not.

Also, more than half of the people who claim Cherokee heritage are not even Cherokee. Often, they are not even Native. This aspect of their identity is the result of family lore, and the claims are entirely unsubstantiated. They have no documents or any kind of paperwork that indicates their tribe, reservation, clans, band, etc, and know next to nothing about their customs. It can be a little old hearing about these ancestral claims when so often, they aren't true.

I am not saying you do these things. You sound like a really genuine person, and you should absolutely be proud of who you are. Research your Native ancestors, because they are a part of you. Where the reactions you are referring to come from are the vast majority of people who say "I'm part Cherokee" do some, if not all, of the things I have listed. As such, some of us have grown hesitant, albeit a little annoying, with these folks.