Sounds just like my dd and she's 2.5. Sometimes if we've walked half way up the stairs holding hands and she remembers she wanted to do it on her own, we've had to go all the way back down, stairgate shut again so she can start again on her own. We also get a lot of "no, not like that, like this" and at the moment just "no, don't" - which I'm pulling her up on as it is just rude!
I try to let her feel independent by asking her to try to dress herself, get onto the toilet herself, wipe the table, pass me things, mix things up when cooking etc. Probably if I thought about it - the days when I make an effort to do stuff like that, I get less of the angry "no, I do it" comments.
Oh and I often just ask her which cup she wants - I'm not bothered which she has but she is often extremely bothered! Sometimes she has her drink out of a little cup from her tea set ... as long as she's drinking I'm happy and she's happy cos she's got what she wanted. I choose which cup I want (and I have my favourite) so why shouldn't I expect her to want to do the same?
So in short, I agree, it is frustrating. Everything takes 10x as long ... and on those days when everything I do is wrong I just have to bite your tongue and try to give her the responsibility - "OK then, you show me what to do" and try to tune out the lecture I'll get ... "mummy you put it in that box but it should go in this box, not that box, you shouldn't put it in that box, no, it goes in this box" etc etc etc.