The phrase is normally heard in circumstances in which it means precisely "I have a right to be selfish"; by those walking away from their family to indulge in a hedonistic sexual fling, by those who steal, cheat, breach oaths and promises and ride roughshod over moral fundamentals to accrue wealth, fame or a prolonged state of inebriation or drug-hazed fatuity, or by those who run from their responsibilities to others for their own sakes.
Every time you hear it, reader, whether on a TV soap, mouthed platitudinously in a newspaper interview, or from some vapid addle-brained shop-girl on the tube, I urge you to say quietly "I have a right to be selfish".
The fault of course lies with the wording of the US Declaration of Independence. "Life, Liberty and the pursuit of happiness" is not an invitation to nihilistic hedonism, and the thought that this phrase was being used to excuse the most immoral of behaviour would leave the founding fathers spinning in their graves. The clearest explanation of the context of 'happiness' comes I think from Adam Ferguson;
If, in reality, courage and a heart devoted to the good of mankind are the constituents of human felicity, the kindness which is done infers a happiness in the person from whom it proceeds, not in him on whom it is bestowed; and the greatest good which men possessed of fortitude and generosity can procure to their fellow creatures is a participation of this happy character. If this be the good of the individual, it is likewise that of mankind; and virtue no longer imposes a task by which we are obliged to bestow upon others that good from which we ourselves refrain; but supposes, in the highest degree, as possessed by ourselves, that state of felicity which we are required to promote in the worldTrue happiness, to abuse another platutude, comes in other words not from what you can screw from your country, but for what you can do for your country and your people.
Finally, I must declare a certain sympathy for the words of a Boer father from some half-remembered novel to a son who was leaving the farm to go to Cape Town to be gay, on the basis that he had 'a right to be happy'. The response was something like "You have no rights other than the rights to fulfil your duties; to serve your nation, to love the Lord your God and to honour your family".