To say that x is the only thing that should be pursued as an ultimate end, implies that x is the sole instrinsic value. This implies that John Smith's happiness is the sole intrinsic good. Therefore, egoism implies that there is more than one sole good, which is contradictory. A property that an object has, independent of the attitudes or beliefs of observers. The view that there are some objective values, or some objective moral truths.
Goodness is objective and definable in terms of non-moral properties.
Goodness is objective but not definable. We know about it through moral intuition. People make mistakes in intuitions, just like they do in perceptual judgements, memory judgements, and everything else. E.g., there are some circumstances in which it is ok to kill a person. Therefore, they are not objective.