What he can do is tell the IRS to go through the existing rules and find a reason why Harvard doesn't qualify for tax-exempt status. The problems will be that, first, whatever the reason given will be, it will head for a court case, and second, it will be almost impossible to interpret the rules so that the new interpretation hits Harvard only (and not, say, the other Ivy League schools).
No. Even this is illegal. There's specific legislation about this, which explicitly covers the president. The president is not allowed to tell anybody at the IRS to investigate any individual person or organization.
Harvard defied Trump and that's why they're making this push. I don't think any given argument to the feds will change that math.
If you work for the feds, I think you know that if you were to follow a process and find that Harvard should retain their tax exempt status then you won't have a job long.
Harvard who doesnt control their grads go on to become supreme court justices and other politically appointed positions.
Harvard takes blame?
Now they are digging deep to find other reasons to attack harvard?