I behave the same way around other people: when offered assistance, I counter with "I can totally do this, thank you but I'm fine," but when no hand is held out, my mental dialogue vibrates with a self-righteous "oh my god I'm exhausted why on earth would you think that I could carry a plate of food by myself."
In school last semester I learned about cognitive dissonance (or rather, I was finally given a name for it): the act of holding two opposing concepts in our minds at the same time. Our human dislike for this jarring, discomforting sensation often leads us to validate one idea over the other for the pure mental relief, regardless of actual value. "I am a regular person just like you/ My needs are special and must be acknowledged" is my dissonant song lyric du jour. I can go to the store and carry a shopping basket, but when someone holds the parking elevator to squeeze in an extra couple and their cart, I exude irritation from my pores and shift to make sure everyone can see my cane.
F. Scott Fitzgerald said "The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time and still retain the ability to function." I'll keep working on the function part.