How to Understand the Gap between the Chief Good and the Good in Aristotle's Function Argument

Aristotle seeks to find what happiness(eudaimonia)is for human beings in
his Nicomachean Ethics. He specifies that happiness is the chief good, and
divides goods into several kinds according to their degree. Some goods are
dependent on and means of other goods. The chief good is supreme and
complete. However,in his search for happiness, he turns to finding out what
human function is and from then on, he unconsciously or consciously
switches the chief good which is eudaimonia ad he should be searching with
the good. He maintains that the good for human beings lies in their
function and formulates his function argument to find what the human good
is. Yet, what he finds is only human good whereas happiness is the chief
good and Aristotle equals the human good with happiness in the end of the
function argument. How would this gap between human good and the chief good
be understood in his function argument? Is it a problem with his argument?