Most of what we do in life is the result of try and error. From learning to walk to riding a bike or playing an instrument, we understand that we have to try many times before we get it right. I think that we internalize the idea of failure when society exhibits our errors in contrast to others.
Individual differences and "accidents" will make different people perform differently at certain tasks or goals and it is in the comparisons of those results that we may draw our sense of inadequacy.
Also, I think that the idea of failure is associated with time. How munch time was invested in the goal? Can the goal be attempted again?
Trying to get the right cookies may not take so much time and effort; trying to raise our children again (asuming we judge the result a failure) may be simply impossible. I have seen many parents in their old age lament their failures at trying to raise good kids (especially when they get criminals or ungrateful children as a result). Of course, this feeling is aggravated by the comparison effect. The grass always looks greener next door.