"We want everyone to have a chance at school, but public schools are government indoctrination so we'll just make sure people are in un-releasable debt to private companies."

"We don't want to see people dying in the streets, but universal health care is "socialist", so we're create these convoluted insurance systems, but still require hospitals to provice free ER care (that has to be covered by everyone else in the end)."

"We're afraid of immigrants, but our agricultural industry is dependent on their cheap labor, so we'll make legal immigration difficult, and keep pretending that we're going to restrict illegal immigration, but never actually do anything effective to curb it."

(I also want to add that mentalities like this are not at all exclusive to the US - you can find similar inconsistencies in every countries self-image, the US just seems to have them in more fundamental issues that other countries made a decision on long ago)