"Fuck that" is a phrase meaning literally "not that". The speaker coherently communicates negative sentiment. The phrase itself, though, is very versitile. Depending on inflection, context and tone of voice, "fuck that" can mean a number of things.
Said quickly and without emphasis, it could be an synonym to "nah" or "no way".
Shouted though, it takes on a more passionate and much angrier light, implying intense loathing and rage. As would, "this is bullshit" or "no fucking way".
Said slowly, with dragged out vowels, it becomes more sympathetic, likenable to "oh that sucks" or "aw man".
When used to refute a point, it can become the opener to an argument, used in the place of "listen to what I'm saying" or "check this out".
A nonchalant "fuck that" is the most nonchalant things one can say.
"Fuck that" is completely and totally punk rock.