States pay for education, Federal pays for military. The Federal government isn't responsible for funding education, so it is unsurprising that they have a relatively small budget for it.

It's a well known fact that US supremacy is mainly due to their military power, but, for example, they lack behind in many other areas, even compared to not completely developed countries like China (that invests a lot more in education[1][2] and cultural products[3])

[1] the United States spent 2.6 percent of GDP on total expenditures on education institutions

[2] public expenditure on education in China amounted to around 4.22 percent of national GDP. That value increased from around 2.5 percent in the mid-1990s to above 4 percent in 2012

[3] China is now the lead exporter of cultural goods, followed by the United States. In 2013, the total value of China's cultural exports was US$60.1 billion; more than double that of the United States at US$27.9 billion.