I am a theologian.
I say that is is a natural right.
We have a natural right to self-defense. That necessarily means that we also have a natural right to the means of self-defense. To say otherwise is to deny the right to self-defense in the first place.
Also, Catholic theology prefers not to use the term “rights.” But instead speaks of justice.
There is no justice in arbitrary gun-control laws that serve no legitimate purpose.
2265 Legitimate defense can be not only a right but a grave duty for one who is responsible for the lives of others. The defense of the common good requires that an unjust aggressor be rendered unable to cause harm. For this reason, those who legitimately hold authority also have the right to use arms to repel aggressors against the civil community entrusted to their responsibility.
“those who legitimately hold authority” can bear arms. That might sound like only the police and military. But a theologian sees it otherwise.
The authority of the government comes “from the consent of the governed” (to use an American phrase). No civil authority is legitimate unless it is exercised on behalf of the people.
In philosophy and theology, we say “one cannot give what he does not have.”
Therefore, in order to “give” civil institutions (ie police, military, etc.) the authority to carry firearms, the citizens themselves must have this authority. They cannot give what they do not have; if they give it, then they must have it.