I think it is more productive to understand the "federal budget is out of control" argument in its spirit and motivational effectiveness. The simple fact is that many people are unhappy about HOW the money is spent and would rather reserve the choices on how to spend that money to the households.
To respond to your specific callouts, the growth of federal programs in the post WWII era is a fundamental point of contention. Averages going back to the 1970s (pegged to GDP of all things) are somewhat beside the political point. The federal bureaucracy is enormous. The ancillary industries that service the federal budget is prone to grift, graft, and corruption. Anyone who has worked in or near Washington DC knows this.
I believe you are talking about Social Security, which is a bit different from "taking care of the elderly." It is more like a public pension. Historically, no country in the world would have spent 36% of its budget "taking care of the elderly" because families, churches, and charities served that function, when necessary. Your framing is already misleading but let's go on.
Combining "defense and veterans" is also misleading. I believe somewhere south of 5% goes to Veterans Affairs (if that much). If you think the US government should spend 15% of its budget on its war machine and the inevitable foreign wars that feed the military industrial complex, we can have that discussion. I don't think 15% of budget is an absurd amount to maintain a global empire, but I assure you it won't be cut all that much.
"Taking care of the poor and disabled" is also a misleading number. Much of that is towards the "welfare state" which is a very gameable and corrupt program. Even if you remove all the outright fraud, reasonable people wonder why a healthy, wealthy country should incentive people not to seek work or to have families out of wedlock and become perpetual wards of the state, as the programs (as currently constituted) promote. And if you think the corruption only helps the poor, you are ignoring the many services that benefit from a large pool of welfare recipients.
Health care costs in the US are too high, but there are many perverse incentives at work leading to those costs that would be tedious to go into here. You cannot begin to fix them without removing the main sources of cost. One is that the population is unhealthy, but also over-medicalized. If Medicare can't negotiate costs by law (remember that battle?) the it is hard to bring down prices. If you want to have a good morbid laugh, take a look at the pricing sheet from a hospital one day. You don't charge that kind of money unless you have someone by the short and curlies.
Corporations are the employers of the workforce. Many are also owned by you and me as common stockholders in our 401k and other savings. You say they are declining as a percentage, but that says nothing about what the optimal percentage is. Too high and you will choke off dynamism and job creation, and drive industry overseas. Who does that benefit?
But all this penny-counting is a distraction. The political motivation for shrinking the federal government is as American as apple pie. As the recent political realignment suggests, most people don't want to be governed by this a federal bureaucracy (or civl service, if you prefer) that has its own political interests at odds with the rest of the population. Centralized power is very susceptible to grift and corruption. It's useful to point out "waste" in terms of inefficiency, but more revealing to point out spending at odds with the values of the majority of the population. People may not want their tax dollars spent on projects they find diametrically opposed to what they value. They don't want to be "pay pigs" for a vast patronage network that extends well beyond any benefits that come back to them. It is at those moments that people start to think that the government isn't working for them. Is that so hard to understand?