I'm curious what your source is for that, because that's pretty remarkable, especially given the outcry about out-of-control military spending.
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.