To answer the question from the point of view of the historical reason for why the act of censure was pursued I believe it is because of pure and simple politics:
General Frank Blair has resigned his seat to the House, and the President has revoked the acceptance of his military resignation. This is a stretch of power and construction that I do not like. Much censure will fall on the President for this act, and it will have additional edge from the violent and injudicious speech of General Blair denouncing in unmeasured terms Mr. Chase. He also assails the appointees of Chase, and his general policy touching agent's permits in the valley of the Mississippi as vicious and corrupt. I have an unfavorable opinion of the Treasury management there and on the coast, and there are some things in the conduct of Chase himself that I disapprove.
Diary entry of Navy Secretary Gideon Welles, 28 April 1864
Chase in the above refers to Lincoln's Secretary of the Treasury Salmon Chase (later Chief Justice of the Supreme Court Salmon Chase), whom Congressman Frank Blair had just attacked from the floor of the House of Representatives the day before. The stink between the two at the time seems to be centered on the existence of a possible forged requisition form signed by General Blair that had been altered from requesting $150 worth of goods to somewhere between $8,000-$10,000 (those figures are sourced from Mr. Welles' diary, so I assume them to mean 1864 dollars). From here:
On April 27, 1864 Congress Frank Blair, brother of Postmaster General Montgomery Blair, attacked Chase in a speech in the House of Representatives – as he had done in February. Historian Daniel J. Ryan wrote: "Lincoln's attitude was friendly enough towards the Blairs that in April, Chase, thoroughly infuriated, still again threatened to resign and to go to Ohio to rally opinion against Lincoln and the Blairs. He was, however, persuaded by Governor John Brough to withhold his resignation."
Supposedly Chase was encouraging this scandal, and, having his honor stained by rumor being too much for him, General Blair resigned his seat and Lincoln immediately reappointed Blair to his old Army rank without getting the required consent of the Senate. From Lincoln's point of view he wasn't creating a new general he was instead simply withdrawing his acceptance of Blair's resignation of Army commission.
The senate disagreed, and it was the absence of consent which caused them to vote to censure.