Giving your citizens the RIGHT to keep and use arms is a vital part of ensuring freedom and that tyranny by government or invading armies is terminated at the will of the people.
Would the British have invaded India had everyone been armed like the US citizenry is? I seriously doubt it. The army would have been liquidated by the people in short order. It would be suicide to invade a country of that many armed people.
This is why we have a right to own them. Because armies invade and governments become tyrannies.
Your narrative of British invasion of India is plain wrong. Also if the USG decided to become a tyranny there is nothing that the citizenry can do about it in this far and age. Guns or no guns.
There are other ways of protecting people and their rights other than having animals roam around who will shoot whenever there is conflict of interests(I understand that not everyone is like that).
Britain could have never conquered a fully united India, the same way it couldn't conquer China (though it chipped away at it for the better part of a century).
Regarding invasions, who's going to invade you? Canada? Mexico? Even if someone wanted to/could, they wouldn't be afraid of your personal weapons but instead they'd be afraid of your nuclear arsenal, of the largest navy, airforce and military budget in the world. A military budget equal to that of the next 10 countries.
All your guns do is promote unreasonable policing practices where people are shot on sight cause you never know if a suspect is carrying a gun. Oh, they also have a great side effect: if you ever have major internal problems or say, a civil war, millions of people will die cause everyone has a gun. Not that a lot of people wouldn't die either way, after all we've been using knives and machetes for millenia, but there's a reason all of today's armies use guns as the main infantry weapons.
The British never "invaded" India. This is a common misconception about Colonial Rule in India. Read about the "Company Rule in India" to understand better: https://en.wikipedia.org/wiki/Company_rule_in_India
TLDR: The British established the "English East India Company" in 1600 to trade with India and did well for almost 150 years. The British had made friends with local princes and nawabs promising them protection if they allowed them to establish their Company. During the same time, the Portuguese, French, Dutch and Danish began to establish their businesses in other princely states of India. This caused friction between the British and the rest causing civil wars to break out. These wars continued for almost 200 years more and involved princely states fighting each other for the benefit of the foreign companies established in their states.
This in turn caused weakening of the princely rulers and strengthening of the foreign companies which commanded garrisons (supplied by the princely rulers) and funded by their business. This shift in power was instrumental in the British devising the Annexation policy called "Doctrine of Lapse" which was signed by these unsuspecting satraps. The doctrine basically stated: "Any princely state or territory under the direct influence of the British East India Company, as a vassal state under the British subsidiary system, would automatically be annexed if the ruler was either "manifestly incompetent or died without a male heir"." This along with the "Divide and Rule policy" enabled the British to establish a Colonial rule in India. All battles the British fought were through proxies (loyal princely satraps) and very rarely did the British actually involve in the fight. Once the Colonial rule was established (powers of the Company were transferred back to the Crown), the British started abusing their powers which in turn caused a surge in Nationalism (read about the First War of Indian Independence of 1857) which eventually ended in the Independence of India (in 1947).
The British technically never waged a single War (there were small skirmishes/battles) with India because that would have triggered all princely states to come together and fight them.
The whole idea of current united India came from opposing the British Rule. Before that, India was just numerous bunch of small kingdoms ruling their own tiny part of current India.
British entered India as East India Company, a trading arm of Britain, which I think is wholly independent of Britain in its ability to rule (politically and military wise) the parts of the world where it had trade operations.
You should also note that Britain had America under its control before US gained independence. If we just extend your logic, then you mean, US got independence just because all of its population were carrying a gun, and not because of strong will shown by personalities like Washington to have an independent nation.