If you add up all the entitlement programs (Social Security, Medicare, Medicaid, etc.) you'll notice they account for more than 60% of the federal budget. Not sure this leaves a 'vast majority' to fund wars.
Those are not (supposed to be) paid through our income taxes, that's why we get taxed medicare and social security separately. The "vast majority" description does apply if you look at non-discretionary spending.
Edit: I suppose it could be argued that money that goes to the military doesn't directly mean funding wars. We have bases all over the world after all.
