Why did Harry tell Snape's secret to everyone?

(Too long for a comment, hence posted as an answer.)

On what basis do you rest the claim that "Professor Snape specifically wanted to keep [his love for Harry's mother] a secret"? As far as I can tell, (a) Snape's love for Lily was never a secret and (b) at no point did Snape make Harry promise to keep this (non-)secret.

When Snape, Lily Evans, James Potter, Sirius Black, Remus Lupin etc attended Hogwarts, it was widely known that Snape admired and loved Lily. Voldemort too knew that Snape had been in love with Lily. Not much of a secret, this piece of knowledge... It is probably true that not many people knew the reason for why Snape's Patronus was a doe -- that Lily's Patronus was a doe too. However, that's just one -- admittedly very tangible -- proof of the strong feelings Snape felt for Lily, not a revelation of the underlying secret.

For sure, Snape made Dumbledore promise -- immediately following the deaths of Harry's parents -- that he (Dumbledore) would never let Harry know that Snape was committed to helping Harry survive and succeed. Importantly, though, Snape extracted no such promise before giving Harry his memories as he was dying from Nagini's bites. Harry was thus free to make use of the memories as he saw fit.

The two preceding paragraphs are based on the very end of Chapter 32, "The Elder Wand", and on Chapter 33, "The Prince's Tale", in HP7.

One thing to consider is that Harry is in a fight for his life. I think he would have grabbed any tool that was available to him. He was thinking on his feet.

There is another thing to consider relating to whether his revealing of this (somewhat open, arguably) secret was respectful of Snape or not. Harry's entire picture of Snape had just been radically rewritten--inconceivably rewritten, probably--and, for all we know, Harry was honoring Snape's memory, recognizing that his incredible courage was sourced, fundamentally, from the greatest of all possible motivations.

It seems likely to me that he is throwing Snape at Voldemort as an example of greatness in the same way that he just previously threw Dumbledore at him. He is presenting Dumbledore as someone who had the capability to do what Voldemort did, but the wisdom not to. And he is presenting Snape as someone that would go to incredible lengths to be loyal to someone that he loved, at great personal sacrifice. Snape and Dumbledore both laid down their lives to save Harry; Harry could, in his mind, be paying the highest honor he could to that memory.

Harry knew that he could not let Voldemort win at any cost, as it was not just a battle for Hogwarts but a battle for the whole Wizarding and Muggle communities. This is not the first time they had come face to face, and it was not just because of Harry's own wizarding might that he managed to stay alive in their previous encounters.

• He survived as a baby after taking a direct hit from the Killing Curse of Voldemort at his forehead; the curse was not only ineffective but managed to send Voldemort into hiding in a highly weakened state. Harry, as a baby, of course did not control this win.
• In Goblet of Fire, the power of their Wands prevented Voldemort from making the strike, and then the memories of Harry's parents took shape and delayed Voldemort from taking a second strike as the Wand connection broke away. Harry was on the retreat, quickly disappearing with Cedric's body as another Killing Curse narrowly missed him. Again Harry did not fully control this win.
• In The Deathly Hallows, Voldemort made the strike in the Forbidden forest at point blank range, but Harry survived that Killing Curse too, where he offered no visible resisting spells back at Voldemort. Harry walked into Forbidden forest not armed with an attack plan to win, he offered no fight, and was giving himself up for the sake of the rest of the world.

But in the final battle Harry would have realized the meaning of his past wins with Voldemort. Harry now would be a fool to not realize that he cannot defeat the mighty Voldemort in a head-on duel with the handful of spells he knows, as compared to Voldemort's huge arsenal of destructive spells. In all the three instances mentioned above, the common factor was the invisible protection of his parents, binding to his body, especially Lily's. He knew that if there is one thing Voldemort couldn't comprehend fully with all his wizarding might, it was the unknown, invisible protection of Love, the white divine magic that could resist all destructive dark spells. And again it was this concoction of Love and emotions inside Harry that prevented Voldemort from possessing Harry for too long at the battle at the Department of Mysteries in the Order of the Phoenix.

He walked to the final battle knowing that Snape who was Voldemort's right-hand man was in fact Dumbledore's man through and through. And that Snape had an undying Love towards his mother and caring for Harry that remained till his last breath. He knew that by letting Voldemort know about his trusted man's true credentials and its underlying tale of Love, he would be reminding Voldemort again about the power of Love, the magic he never was able to fathom, one which he not only despised but perhaps even feared, and by re-confirming its existence to him using Snape's case was perhaps one of the most powerful weapons he could unleash against him.