I'm saying that, based on the previous ruling of the Supreme Court, he cannot use it as he did. In US v Nixon, the SC stated that executive privilege was not blanket immunity. It could only be applied if a valid reason was provided. The Trump administration has provided no reason at all and has declared blanket immunity from any subpoenas related to Ukraine - this is, to me, a clear violation of the precedent laid down by US v Nixon, especially in light of the fact that some material requested by the House has since been released under FOIA requests (meaning that it wasn't actually privileged information).
I'm torn on whether the House should have gone to court over it. On the one hand, I want this information to see the light of day. However, I am concerned that the Supreme Court, in its current form, would rule in favor of the President despite the clear precedent. Kavanaugh has stated before that he disagrees with the ruling in US v Nixon, and the conservative members of the Court have largely ruled in favor of increasing Presidential powers. I'm also reasonably certain that the case would have been tied up long enough that the impeachment trial would not have finished before the 2020 election. There is precedent for expediting the case to the USSC (again, US v Nixon), but that requires the consent of the Court.