There really isn't any non-discretionary spending. The closest we have is payments specified in international treaties, and even that can simply not be paid. All the rest is just a couple congressional votes and a presidential signature away from being eliminated.

Medicare, Medicaid, and Social Security are considered mandatory spending because politicians tend to like being reelected.

That and it doesn’t go through the standard appropriations process.

Discretionary spending is about 1/3 of the budget, and, yeah, defense is half of that, but when the GP wrote that "military spending takes up more than half of the budget" it paints a misleading picture.