People ship it for lots of reasons, every person is different and because of that their reasons are different. Some people ship them because they’re hot and like the idea of them being hot together. Some people pair them off as the last remaining singles
I personally tend to use the analogy of “kintsugi”. Kintsugi is a Japanese art form where broken crockery is mended with clear resin mixed with powdered gold to create a gold seam, it is the art of making something useable and beautiful out of something broken.
Stiles and Derek are both, indiviually, a mess, but they come together to fill in those spaces in each other.
One of the big signifiers in this is touch.
Derek, like most abuse survivors, is very controlling of touch. He doesn’t let people touch him and hides it by touching them, he is the one to put a hand on the shoulder, he is the one who grabs and pulls someone out of the way. He controls who touches him and how, and for the most part no one gets to touch him without him being in control.
If you look at the Braeden sex scene you can see this clearly, he is totally in control, in contrast to the Jennifer one where he is clearly whammied because he has no control. Then when Boyd died Stiles touched Derek. This wasn’t the first time (he touched him in the jeep outside the sheriff’s station and nearly lost the offending hand) but Derek doesn’t shirk off the gesture, or pull away, or threaten Stiles, he lets him touch. So, when Braeden goes to check on Derek’s wound whilst he’s sleeping Derek snaps awake and moves out of reach, Stiles manages to wake him several times with touch.
It’s a simple thing but it’s actually a really big deal.
Then there is the power of human love scene.
In 210 Peter gives the power of human love speech, and on the word love the camera goes from Derek to Stiles (on the lacrosse pitch) to Lydia to Jackson.
Derek, if we trust the cinematography, loves Stiles, Stiles thinks himself in love with Lydia (which we know he’s told us, at length) but Lydia loves Jackson
it shut down the love triangle hard long before the removal of the red thread from Lydia’s finger which was it’s death knell.
Derek, for all his protestations to the contrary, trusts Stiles, in many ways more than Scott, and you can make a solid argument that Stiles was working with Derek over the missing summer (although it’s not explicitly confirmed in the text), but Scott knew nothing, but the big point is that Stiles is comfortable with him, to the point of teasing him, which he would not have done in season 2
Stiles keeps Derek’s secrets, and by the pool scene Derek sees Stiles for the first time as someone who doesn’t judge him negatively for being a wolf, when he says the word “abomination” we see Derek completely undone - by Stiles. He also, on more than one occasion, takes the blame for wolfy shenanigans.
This happens a lot, there are scenes which are, for their lack of clear romantic intent, really intimate between them. Derek takes the role of sleeping beauty to Stiles’ prince, Stiles is the one to wake him (three times now)
this trust doesn’t exist between any of the other characters, Scott and Stiles have been together forever and so fall into the other’s cadences, Stiles will take a bullet for Scott in a heartbeat because he’s his best friend, (we saw him do that with Gerard in 212) but at the same time we know that Scott becomes so bogged down with what’s going on he misses Stiles. Scott didn’t trust Allison (the rave scene) and tried on a few occasions to cow her into submission. Isaac doesn’t trust anyone. Lydia and Stiles are falling into the role of each other’s best friend, but it’s not there yet, but it IS there with Stiles and Derek and has been since season 2.
So we have two characters, who are both broken, coming together to strengthen each other’s weaknesses in a way that is sometimes romantic and sometimes so damn intimate (without being romantic) it’s lovely.
There is an expectation in fiction that love stories fall under what the greeks called “Eros” or “romantic love” but it should be mentioned the word “Erotic” comes from this and as I pointed out a few metas ago, the idea of romantic love as we know it is barely a thousand years old and a western ideal. In the older stories Eros was a lustful love, it was about possessing someone sexually.
In contrast there is “Storge” or the affection, the love that grows over time, not the bang crash of love at first sight, but the love you wake up one day and realise you’ve loved them you’re whole life, and Sterek is Storge, where Scallison was Eros. It’s the slow, natural progression of two people coming together to make each other stronger, rather than the mad passion of two people tearing each other apart
but the vast majority of love stories we get are Eros, when we talk of the great love stories they are Eros, and often it’s because they’re Eros everyone ends up dead, but when you read “they will grow to love each other” that’s Storge. So Arwen and Aragon was Eros, but Eowyn and Faramir was Storge.
But everyone has their own reasons for shipping it, and they look hot together is just as valid as they have a deep and abiding love for each other.