Everyone gets shipped. Even siblings, be it gay or straight. Others are downright surreal, like Draco getting Harry Potter pregnant. I remember we had someone here--
which I point out with no criticism intended at all--that liked the idea of shipping Buffy with Sid the puppet.
I've pondered this for years as it puzzles me so (and I tend to be amused by it as long as it doesn't get hostile, hating people who don't like their ships, or like that disturbed person who hated on Buffy for preferring Bangel over Spuffy). I think there are many reasons involved (which is to say not everyone does it for the same reason), but I have noticed that if they tend to follow a formula then they will be shipped hard. One brother/sister pairing (Justin & Alex in Wizards of Waverly Place) became so pervasive after the movie that Disney actually forced the characters into other relationships to counter it, but to me it was a natural consequence to the movie that followed a formula, the same type of formula that got used in Frozen that had me walking out of a first viewing knowing Anna & Elsa were going to be shipped hard. It's the standard romance formula, but it's usually not intended, in which the characters bicker but grow close through trying times, show uninhibited affection for each other, and one saves the other (or they save each other). Put another way, had Alex and Justin NOT been siblings who went through the same adventure, and same for Elsa and Anna (especially if one were a man), then the audience would've been WTF and unsatisfied that it didn't end in a romantic pairing, because that's how those stories are supposed to go.
I think contributing to this is that passionate love is so heightened and promoted as necessary for happiness while familial and friendship and even purely platonic loves are devalued if not even held in contempt, so that the pay off means there MUST be romance.
There might be a bit of the forbidden relationship and "star crossed lovers" at work as well, though gay romances aren't as forbidden as they used to be, but still controversial (and can thus be inserted strictly to raise controversy which will raise viewership, and thus make money). This also makes for easy drama which draws audiences in and gets people tense to see how it works out. Perhaps writers and readers and viewers like it because it's a safe way to explore relationships in a way they'd never dare in real life (even if they're not particularly interested in doing so at any level there can still be curiosity about it).
And let's not forget that's how people are in every other way as well. I'm sure you remember it from middle school on up if you went to school on constantly talking about who likes who, who'd you "do," who you marry. I remember playing
MASH as young as 10 years old with other girls (and some of them had been playing it for years by that time). And that obsessive interest something many never outgrow...just watch the news and tabloids, people still want to know the same stuff about who's screwing who, who's dating whom, and all that, and typically gossip about that on the people they know (guys seem to do it as well). There's a common game on the internet on who you'd go gay (or straight) for, and of course the Marry, Shag, and Kill game. There seems to be an obsession on figuring out who's secretly gay as well...I recall how some people about celebrated as "vindicated" when Jodie Foster came out.
That is, romance and/or sex greatly interest people, especially that which is a bit odd, and just as many constantly wonder about who is hooking up with whom in real life, they do it with the characters they care about in fiction as well. And when you do it so much, some of them will inevitably be gay, and may be fascinated with gay pairings in particular just as people tend to be fascinated in figuring out who else is gay in real life.