If you are unwilling to do something, you do not want to do it and will not agree to do it. Initially the government was unwilling to accept the defeat For months I had been either unwilling or unable to go through with it. willing + unwillingness un·will·ing·ness their unwillingness to accept responsibility for mistakes
You can use unwilling to describe someone who does not really want to do the thing they are doing. A youthful teacher, he finds himself an unwilling participant in school politics = reluctant + unwillingly un·will·ing·ly My beard had started to grow, and I had unwillingly complied with the order to shave it off Unwillingly, she moved aside. = reluctantly