Quoted:Genisis 9:13
13I have set My rainbow in the cloud, and it shall [h]serve as a sign of a covenant between Me and the earth.
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Proverbs 16:18
Pride goes before destruction,
And a haughty spirit before stumbling.
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I know how these passages are traditionally viewed. And never have I heard them mentioned together that I can ever think of. However would it be not like God to use those who claim to be against him in order to get his message out? I often pray that God would make himself more visible, his message more clear. And everywhere we look we see "Pride", and the Rainbow together.
Coincidence?
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An interesting question.
Keep in mind that Satan apes/mocks the divine and good, and so too do his minions.
I recall reading, though I cannot recall where exactly, that one of the big reasons for the Flood was the proliferation of sodomy, bestiality, and incest. Hence, it is fitting that a mocking symbol of such a milieu would be the symbol of the rainbow, which is related to the Flood.
As far as pride understood biblically (being above what one is), this is not exactly what the homosexuals mean in a pure manner though they do exhibit it insofar as believing themselves superior to us lowly "breeders". And, in doing so, do exhibit the vice of pride.
St. Thomas Aquinas defines pride as:
I answer that, Pride [superbia] is so called because a man thereby aims higher [supra] than he is; wherefore Isidore says (Etym. x): "A man is said to be proud, because he wishes to appear above (super) what he really is"; for he who wishes to overstep beyond what he is, is proud. Now right reason requires that every man's will should tend to that which is proportionate to him. Therefore it is evident that pride denotes something opposed to right reason, and this shows it to have the character of sin, because according to Dionysius (Div. Nom. iv, 4), "the soul's evil is to be opposed to reason." Therefore it is evident that pride is a sin.
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ST/II-II/Q162/Art1 (https://www.newadvent.org/summa/3162.htm#article1)
The origins of the Pride events do have an element of diabolical rebellion and disorientation:
It's actually difficult to surmise what exactly motivated Howard and her contemporaries to choose the word "Pride" back in the late '60s as the world the queer community fought to survive in was much different; unfortunately, there is no recorded history (or at least, not that I was able to find in my research) as to why Howard chose "Pride"and why the word stuck so firmly. It's worth considering, though, when we look back on the meaning of the word "pride" itself and its usage within the queer community, just how different society was at the time of the Stonewall riots. For instance, people were regularly jailed for homosexual activity, sent to mental institutions to "cure" their sexuality, and shunned by their families and communities for coming out. In many ways, Stonewall was not a celebration, like many contemporary Pride events, but a revolt against oppressive laws and stifling societal values — a revolt that encouraged us to speak up proudly instead of hide ourselves away.
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https://www.bustle.com/articles/167359-why-is-it-called-pride-heres-why-the-name-of-junes-lgbtq-festivities-is-significant
What began as a rebellion culminates in a "celebration", not of
being higher than the other(society), but of
dragging down society so that it engages in inordinate subservience and a cloyingly saccharine level of being obsequious. In reality, the homosexuals have never engaged in an ontological shift "up". They *cannot* reproduce unless they "lower" themselves, they *cannot* escape the reality of self-hatred, they *cannot* be content with tolerance and have moved towards force acceptance (which will not be good enough since it has the same character as a forced apology), etc.
But, as far as your thought on the connectedness of the two verses, it is unlikely to be anymore than a weird coincidence.