Toppling the Ivory Tower
I have called the extreme right "Unreasonables" and asserted that they are waging a war on rational thought. The "conservative" attack on the university is probably the single best piece of evidence for this argument.
Given the recognized importance of a college education for social mobility and America's economic competitiveness, why would the right make such a determined effort to undermine the university? There are two complimentary objectives. First, to eliminate one of the last bastions of "liberal" (i.e. independent and rational) political power. While they would prefer to co-opt the academy into the right-wing propaganda machine, they will settle for destroying it entirely.
The second objective is more unconscious. For the right, the entire project of the academy is insidious. The purpose of university education is to develop critical thinking capacity, which is inherently questioning of authority and tradition. This goes against the essence of the conservative political project. And because it is a vehicle for social advancement by the middle class, it creates competition for the scions of the rich and powerful. Giving money to universities amounts to a subsidy to the middle class at the expense of the elite, which is anathema to conservative political ideology.
The right's strategy is quite clear: bully, de-fund, and de-staff the academy in order to restore its 19th century role as a finishing school for "gentlemen." It is just one more way in which the right is demonstrating that it hates America - the America of the 20th century, anyway.