It sounds like you got yourself a 'one of me.' I'm certain that if I had been my grandmother's daughter she'd have beaten me to death, and then sworn that I'd provoked her to it on purpose. Fortunately, I was my mother's daughter and my mother figured out before I was three that she *could* spend the rest of every moment of ever day having a non-stop argument with me... or she could, well, just not.
My mom says that she had *NEVER* encountered a more determined, argumentative, unbribable, non-compliant, resistant human being in her life. To date. Since my mom would rather eat her own feet than argue with anyone about anything at all, ever, it certainly wasn't *HER* doing that made me this way. And it was totally overwhelming to her.
As soon as my mom decided which three things she was going to be equally-determined-as-I-was about and stopped pushing me about everything else, I became a mild, easy-going happy little monster. As Barbara Coloroso says: never argue with anyone over the age of 2 1/2, their verbal skills are too well-developed and you will lose.
Edmund Sprunger, Suzuki violin instructor, said: Resistance is the child's way of cooperating by showing the adult what doesn't work.
For me (and the many children like me) caving in to bribery, pressure, demands, the whims of others, bureaucracy (sorry to say that I still haven't outgrown THAT one) and orders always felt TO ME like being asked to give up who I am. Not what I want, not what I think, not what I have -- but myself, at the core.
When you're arguing with your little one, or trying to move her in a direction she doesn't want to go in (or doesn't feel ready for, or is afraid of) TO HER, you may be asking her to stop being herself. For this reason, she'll be so much more tenacious than you are... she has the survival of herself at stake. You just have some diapers or a clock, or what other people think of you. It means more to her, it matters more to her, so she won't give in before you. If you're planning to be equally-determined, expect a very long war.
I recommend you take my mom's advice. I didn't turn out to be a homicidal maniac, I've never been arrested, I have a stable home and family, I've been married to a very tenacious man for 23 years, and most of my friends have been my friends since high school. I still won't say anything I don't mean, and will take no vow I do not intend to keep. So it didn't turn out too badly.
My mom says she realized, somehow by a stroke of miraculous luck, that I was trustworthy, sensible, rational, cooperative and, unless provoked to resist, happy to go along with pretty much anything that was explained to me (rather than ordered at me). I would, she felt, 'probably' be fine, and even if I wasn't, living in a non-stop war just wasn't something she could face, so she literally surrendered. She insisted on bedtime, eating at the table, and going to school.
I never balked on any of those, because I could be awake thinking about anything I wanted in bed, didn't care where I ate and enjoyed school enough, cause my friends were there anyhow. Strangely, the vast majority of teachers I had 'just knew' that I wasn't for pushing around, and not one ever tried more than once. I was fortunate to have some great, respectful teachers.
Mom & I have never argued about anything, ever again. One of the things I love my mom for the most is her deep respect for me, and her unshakable trust in me, which has translated into her being an amazingly supportive grandma.