The bulk of social services spending is social security and medicare, which _each_ account for somewhere between 20-30% of federal spending. Military spending is closer to 15-20% of the federal budget
Essentially you are "both right". > 50% of total spending is Social Security, Medicare and Medicaid. Whether that is "social services" is another semantic question.
And > 50% of the discretionary budget is defense.
But have a look for yourself: e.g., https://en.wikipedia.org/wiki/United_States_federal_budget
This is puzzling to me. I don't think I've ever heard anyone argue that social security, medicare, and medicaid aren't social services. As far as I'm aware, everyone agrees that these are all social services. I would be curious to hear arguments for excluding it from the "social services" rubric.
It's not that black and white, because...
Police slush funds are funded (indirectly) by the federal government—drug search and seizures are passed off to the feds to prosecute (because many states have laws banning the practice), and the feds shares a portion of the value seized back with the local police department. Win-win.
For multiple reasons actually:
From the fact that we could be spending any arbitrary percentage and it wouldn't mean it was enough...
To the fact your 50% number doesn't map to 50% spent of the type of social services they meant. Just because it Social Security has the word social in it doesn't mean it's helping the way these social services would...