So what your uncle is telling you is partly true. During the Colonial era, many parts of Colonies, especially those dealing with Native Americans did have large militias. In many places, especially during the American Revolution, being in the militia for men ages 16+ was mandatory -- although often times people could offer up a "muster tax" in lieu of active participation. However, this wasn't something every American male had to deal with, especially since many communities (especially in the South) did no openly support the war.

That said, I've never seen a single state or colonial law that required firearm ownership. Firearms were expensive -- many times prohibitively expensive for many working class Colonials. As a result, some militias, such as several in Connecticut and Massachusetts stored firearms at a centered locations and were actually publicly owned. The Minutemen and Their World by Alan Taylor and Robert Gross give some other interesting background information on this if you are interested.

One other thing worth mentioning is that I've also answered other questions on the creation of the second amendment before, which you can check out here Essentially, I explain that most Historians understand that the Founders insisted on creating the second amendment due to the rise of rural insurgencies and rebellions that were popping up in places like Pennsylvania and Massachusetts. They wanted to ensure that members of the local gentry could always call up impromptu militias to combat these uprisings. If you have any other questions, please let me know.