White House complaints over Pelosi not holding a vote for inquiry is just a dodge - 2019-10-09
The crux of the White House's impeachment push-back (as expressed in yesterday's Pat Cipollone letter) is that the House's inquiry is illegitimate because it didn't vote to conduct an impeachment inquiry, which robs Trump's of his due process rights. There have been votes in the past prior to "official" impeachment inquiries in the House.
A few notes on that.
There is no requirement (either in the Constitution or House rules) that the House conduct a vote in order to proceed with an impeachment inquiry. The executive branch doesn't get to define the legislative branch's process.