Coming out is actually one of the strategies gays and lesbians have used to achieve legal equality, and social acceptance.
It is "proud" as in the opposite of "ashamed.
The Stonewall riots in NYC is often marked as the beginning of the gay civil rights movement It took place in 1969, a mere 7 years after this documentary film titled "Boys Beware" about the dangers of homosexuals lurking in your midst.
That film contains the line: "What Jimmy didn't know was that Ralph was sick, a sickness that was not visible like small pox, but no less dangerous and contagious, a sickness of the mind, you see, Ralph was a homosexual."
You could tell lies like that in 1961 because people who were gay didn't come out, nobody thought they knew any gay people, today though it is unlikely that you could make that claim, especially if you live in a city. Gays are everywhere, and it is that visibility that has made it impossible for the right to continue falsely claiming that gays are mentally ill child rapists.
Things have changed a lot, and "proud" may eventually go into the dustbin as more and more people feel they have achieved equality.