That’s part of who Claire is. I won’t write you a long and detailed character analysis (tired at the moment) so I’ll try to keep it short. How do I explain…
First of all, their last name is Fisher. That’s not meaningless - it was chosen because all of the characters are looking for something. Fishing, essentially, for happiness, peace. So you have to keep in mind, Claire is not happy… none of them are. So she complains because of that. I can understand being annoyed because honestly, I hate it when people complain all the time. What you have to understand about Claire though is that she’s trapped and scared. She knows she isn’t happy where she is (a primary reason for her complaints) but can’t really do anything about it either - because she’s still young, has nowhere else to go. She tries to make something of herself with her art later, but that’s not an easy thing to do. Her family is strange, she’s surrounded by death, and she still doesn’t know who she is, really. So it’s understandable she’s a little upset.
But that’s just Claire. She talks and expresses herself a lot. She lets it all out and is very wordy. And it just comes out sounding like complaints - sometimes they are, but other times I think she’s just trying to help herself and others understand what she’s feeling, without the complaining intention. She’s different from her siblings in that way they deal with stress and unhappiness. Claire complains, Nate runs, David bottles.
How I feel about her? I adore her. Her complaining? It can be an annoying part of her character, but it’s very human thing. It doesn’t sit right with everyone but it sits okay with me. You just have to understand that these are very very well written and human characters and that they all make you mad sometimes - they’re not perfect! Just as real people are. We’re not perfect. Part of why I love the show :’) So that’s why I still love her.

Claire: Why did you have to die? It really sucks. Everything’s unraveling since you’re gone.
Nate: That’s not true.
Claire: It feels that way. I miss you. I miss you so fucking much!
Nate: I miss you, too.
Claire: You know how I always used to tell you you weren’t Dad, after Dad died? It was such a waste of time thinking that way.
Nate: No, it’s just part of how you dealt with it. It kept you from missing Dad so much.
Claire: No, it kept me from ever knowing you as much as I really could have, and now you are so completely fucking gone! It’s just …
Nate: Claire –
Claire: What? It sucks!
Nate: Stop listening to the static.
Claire: What the fuck does that mean?
Nate: Nothing. It just means that everything in the world is like this transmission, making its way across the dark. But everything – death, life, everything – it’s all completely suffused with static. [makes static sounds] You know? But if you listen to the static too much, it fucks you up.
Claire: Are you high?
Nate: I am actually, yeah, quite high.
It’s fucking sad and it’s fucked up! I mean, did you cry? Did you?
Because I can’t imagine ever being this dedicated or this consumed by anything.