It can't be true that both universal higher education and immigration are social goods, since it is cheaper to just not educate some percentage your own people.

This comment perplexed me until I realized you were assuming that the average education level of immigrants is lower than that of "natives" (that is, the pre-existing population of the country). But that need not be the case. To borrow from personal experience — many immigrants from the former Soviet Union are quite a bit more educated than the national average in the U.S. Surely immigrants who bring an above-average education with them are good for the society (assuming that they intend to become productive members of society)? Doesn't it follow that both of the things you mention can, in fact, be true, conditional on certain contingent properties of immigration?*

*And of higher education, presumably. I mean, we could say "higher education can't be a social good if we do it wrong in ways X, Y, Z", to which the obvious response is "we shouldn't do it like that, then."

"War is not good for your economy (unless you aren't fighting in it)."

That's pretty well accepted in some economics circles. See the broken window fallacy by Frédéric Bastiat.

It can't be true that both universal higher education and immigration are social goods, since it is cheaper to just not educate some percentage your own people.

Perhaps this is nitpicking, but it's possible for both to be social goods, but one is more of a good than the other.