God, loads of reasons, I challenge any parent to be truly zen about it! I think the foremost 'button' is any parent's natural instinct to nourish and feed their child which after all is the main thing you need to do to keep them alive, most people's no 1 parenting goal! When you know they haven't eaten properly for hours/days and they still won't eat no matter what you do, it's horrible. Worse when they are ill/tired/constipated and the not eating is making things worse but they worse they feel the less they'll eat and so on and so on. It also plays into the fear of being judged that most parents have to some extent, if your best friend/MIL/MN knew that you've been feeding your toddler on nothing but nuggets and plain bread for weeks on end, or conversely they've eaten nothing at all because you refuse to feed them nuggets and bread, you feel like they'd be calling SS on you which is not a nice thing!
Then as others have said there's the feeling of rejection when you've put a lot of effort and love into preparing nice meals that should please the child, and they wail and scream as though you've presented them a plate of slugs or gruel, that really jangles your last nerve! This is particularly bad if you have a 'capricious' fusser, one that will eat something one day with relish and ask for more and then howl and reject it the next day with no discernible pattern
. I think this is partially a power struggle, the slow melancholy process of letting go that starts the day they leave the womb, the steps towards them being more and more autonomous and asserting control over their own lives, it starts with them preferring chips and beans over your lovingly-made casserole and ends with them walking up the aisle to marry that boyfriend/girlfriend you always hated, in both instances you really quite want to firmly correct them (!) but probably best to keep your mouth shut and play along with their ideas 
Then of course there's the practical annoyance of your food and time budget not allowing for them to dictate their own menu 5 times a day (and change their minds in between, and then still call what you give them disgusting!) as if your house was a cafe, and having to spend yet more time and effort storing, binning eating their rejects when you have better things to do.
Basically toddlers and small children are mini despots and exactly as terrifying/sanity sapping to live under, there is no pleasing them sometimes no matter what you do. You couldn't pay me to go back to that stage I'm afraid!