The article recognizes that a "contract" presupposes that each party relinquish something of value to the other voluntarily.
The question then becomes; "What is given up and what is received?"
When a mother bear acts to protect her cubs, we recognize that she acts in her own self-interest. Most people would recognize an obligation not to bring such behavior about.
The mother bear is not expected to understand the true nature of the threat. She may act pre-emptively based on her perception of the mere ability or potential of someone or something to harm her cubs.
Humans are as fully justified as bears to protect their young. However, when we enter into a social contract with others, we choose to voluntarily give up justification for pre-emptive attacks in return for being protected from the pre-emptive attacks of others. The "right" of self defense is not given up. This is a subset of protective behavior which is not pre-emptive but which requires some greater level of threat than mere perception that harm might be caused.
The "right" of self-defense is the residual part of the freedom to act pre-emptively when protecting one's own interests.
This argument reveals a semantic problem with trying to determine whether the "right" is created by the contract or whether the "right" pre-existed the contract.
Our nations Founders believed that we are endowed by our Creator with certain unalienable rights. They had envisioned certain boundaries between the liberties which they expected to retain and the liberties which they had decided to give up by "consent of the governed". All of their liberties were endowments from their Creator.
The right to the "pursuit of happiness" is the nearly boundless liberty of self-interested behavior. That which is outside the bounds are those behaviors which justify non-pre-emptive interference by others.
To define the word "right" to be that which is created by the contract would be to suggest that a piece of pie does not exist prior to slicing the pie. There may be a question of boundaries, but slicing does not create pie.
Our Founders decided that some rights were of such consequence to the successful creation of government that they enumerated specific limitations on what could be given up by "consent of the governed". Without amendment to the Constitution, the people may not allow their liberty to defend themselves with arms to be bounded. Nobody would reasonably suggest that a mother bear had only a "collective" justification to protect her cubs. Nor would anyone suggest that the mother bear should restrict herself to the use of her teeth but not her claws.