For one thing, "happiness" is a subjective thing -- hardly the basis for a supposedly objective philosophy based on the claim that "Reality exists as an objective absolute facts are facts, independent of mans feelings, wishes, hopes or fears."
Rand and her disciples make grand claims to being the "only logical philosophy." If "happiness" is the highest moral goal, then either this statement is invalid, or the "highest moral goal" is not what Rand says it is.
At any rate, the combination of the two claims forms a contradiction -- not what one expects of a truly logical philosophy.
The objection is found in the complete quote:
"We hold these truths to be self evident: that all men are created equal; that they are endowed by their Creator with certain unalienable rights; that among these are life, liberty, and the pursuit of happiness."
-- Thomas Jefferson
Ayn Rand doesn't believe in God or religion. Without religious moral guidance, the "pursuit of happiness" is pretty wide open, wouldn't you say?