Maybe I'm about to stir the pot but whatever here goes: idk why some (obviously not all) Sam stans get so defensive about the insinuation that Dean might be female-coded in some ways (well, actually I do but I don't wanna get into that 😂), but it got me thinking about what it is that some fans see in Dean, and for some female or gnc fans, what it is in Dean that we relate to. (Just for the record, none of this has any bearing on how female-coded Sam is--it's so not a competition lol. I think Sam can be considered very female-coded. Also, for the record--although this really ought to be self-evident--I don't equate female-coding with feminization, woobification, or even softness necessarily, nor innate relatability/sympathy.) Anyway, it led to some Dean meta thoughts:
First, I think a big part of it has to do with emotional labor, particularly within the John-Dean-Sam dynamic. We know that from a young age, Dean was aware of what his father did and was performing emotional labor in caring for his father when he was tired after a hunt (like the "It's okay, Dad" anecdote), or drinking too hard--and being practically the only such emotional support John had/would allow himself. Also, having your sibling's life placed in your hands, being repeatedly told it is your responsibility, is certainly emotional labor. And being in a household with two strong clashing personalities, being forced into the peacekeeper role (as we see echoes of in s1), is emotional labor.
Another obvious aspect (though for some reason an especially contentious one in fandom it seems?) relates to Dean's domesticity and role as a nurturer. I really don't care to argue here about how domestic and nurturing Dean is or isn't, because I think for purposes of this post, it's actually sort of irrelevant. The point isn't that Dean was the best homemaker ever; what's much more interesting to consider is how, in the absence of a female presence, typically "feminine" tasks fell to Dean, whether he was willing or not. Dean says it plain as can be in 12.22 Who We Are: "I had to be... more than just a brother. I had to be a father and I had to be a mother, to keep him safe. And that wasn't fair. And I couldn't do it." Of course he couldn't, because he was just a kid only four years older than Sam. But that doesn't mean that the burden of expectation, that that role was his to fill, wasn't there.
Related to the last point is how Dean suppressed personal desires for the sake of family, which is so often expected of women. It's an extension of the caretaker role; anything he may have wanted must come second to his duty to family. The shapeshifter in 1.06 Skin has access to Dean's thoughts and says: "You got to go to college. He had to stay home. I mean, I had to stay home. With Dad. You don’t think I had dreams of my own? But Dad needed me." In fact, you could easily argue that the only desire Dean ever really allows himself to have or express is family. Opinions on Lebanon may vary, but I don't think it's at all out of character that Dean's greatest wish was for his family to be all together.
I also think that Dean's brand of vulnerability is something that some female fans would find relatable. I don't want to sound gender-essentialist about it and I don't think I would call this female-coding, because it's not necessarily a universal female experience (not that anything that could be considered female-coding needs to be universal--that would be impossible), but I can say that it's probably the primary characteristic that drew me to Dean. Dean's insecurity is rooted in his fear of his emotional needs being too great. He is insecure about how much he needs his family, and worries that that need is not reciprocated (whether it is or not isn't the point--this is about Dean's perception). In season 1, it's his feeling that John and Sam care more about killing the demon than they care about him. For many more seasons, it's his fear that Sam will leave him. He's terrified of being needy, of his emotions and his love being too much. I would venture a guess that within family structures, this is a trait most commonly associated with mothers/wives.
I'm sure there are some more points that could be made (something about performative gender that I'm too brain-tired to write out atm?) but these are what occur to me off the top of my head. I don't think it should be surprising to anybody that both male leads of a show with a large female fanbase have aspects of their characters that could easily be considered female-coded, nor that different fans identify more with one or the other (which may or may not have to do with their individual brands of female-coding. In many cases, I think it does.) Personally, I also think that both Sam and Dean fans sometimes exaggerate these traits to the point of being OOC--and I think that's their prerogative, enjoying fandom as they wish to, though it can be frustrating when it seems like that fan version of the character is conflated with the canon character. But it is silly to think that only one brother can be female-coded or relatable--and for that matter, it's silly to equate female-coding with sympathy points. For some people, female-coding may make a male character more relatable, but female-coding and relatability or sympathy are not directly correlated. In fact, some discussions around female-coding are a little off-putting to me for the implication that any sort of relatable trait in a male character must be be female-coded, or that possessing/showing emotions at all is innately feminine. To me, it's just interesting to observe narrative and characterization trends in a cultural context. But that's a more complex discussion for another time!