It's pretty straightforward, really. Gay 'pride' events were set up under that name because pride is seen as the reverse of shame. The pride events came about after The Stonewall Riots in the States and were a reaction to the idea that the only culturally sanctioned reaction to one's own homosexuality was shame. There was still a great deal of credence given to the idea, even amongst doctors and psychologsts that homo/bi/anything kinky sexuality was something that could be 'cured'; that it was an affliction, a 'leprosy of the soul' of according to one eminent American churchman.
The very use of the term 'pride' was a defiant affront to the religious bigots, the retailers of quack therapies to cure queerness, the name calling bullies. The pejorative term 'queer' was reclaimed (as later 'nigger' later would be by some sections of the black civil rights movement) and the Stonewall Slogan became 'we're here, we're queer; get used to it'. Put them together and you get Queer Pride.
The adoption of the term 'gay pride' in the UK was significant, in part, as reaction to the tone of the legislation that decriminalised male gay sex for over 21s. Whilst the enactment of that legislation was a massive step forward, many were uncomfortable with the tone of the debates and media reporting, which, even when sympathetic to the aims of the legislation, suggested that these poor unfortunate souls should not be punished by the law for their dreadful affliction. So the use of the word/notion 'pride' is historically significant on those terms.
Social attitudes may have changed here, but as a teacher in London I encounter rabid homophobia - often sanctioned by religion - from my students all the time. Elsewhere, e.g. in Poland where the Mayor sought to ban a Pride-style event and when the downscaled event did take place participants were harried, abused and attacks by members of far right and Catholic organisations, the story is very different.
The notion of Pride is about not just about (grudging) acceptance, it is about visibility and equality. I have just had lunch with someone who was talking, very movingly, about his tremendous pride in his (heterosexual, monogamous) relationship which he and his fiance are going to celebrate publicly with a wedding. I doubt you would 'fail to comprehend' that concept of pride. The gay rights movement is trying to achieve the same kind of acceptance for same sex relationships - it is less about saying 'look how special we are' and more about 'look how ordinary we are, look how we are just like you and therefore entitled to the same degree of freedom, legality and indeed, pride, in our relatonships'.
You don't get a more public or open display than a procession through a capital city. In amongst all the disco-titted drag queens and pretty (and not so pretty) young things who view it as a great big party and pulling opportunity, there will be hundreds of people, especially older ones, who carry scars from the queer-bashings they've endured or memories of friends whose lives were deatroyed (some who may even have committed suicide because they could not bear the shame they were made to feel). They will also marvel every year at the changes they have seen and the freedoms that they can now enjoy. Pride is, as you say, very different from a lack of shame, but for the people I'm talking about and for every closeted teenager trapped in a home where the prejudices of the Daily Mail, the Bible or the Khoran prevail, a lack of shame just isn't good enough.
My alternative reply, which I didn't post, was: Maybe someone should stick a cock in your arse - at least it would stop you talking out of it.