I don't really mind a female link just like I don't mind the idea of a female Doctor. So long as the game is strong and it isn't in your face about it then gender is really irrelevant.

As to why others might want it...well, your answer is in the thread I feel. It boils down to wanting a change from the norm, which is difficult to argue against. 

In a game full of magic, fairies, giant mole-ish people, items that defy physics, potions that instantly heal wounds, and immortal wizards with designs of conquering an entire kingdom, is believability REALLY that much of an issue?

Video games are all about fantasy, and people pulling off ridiculous feats not even remotely possible in the real world. I'm not sure how something like a female Link really makes the believability of games all that more unreachable.

Anyway, I've seen some feminists advocate for a playable Zelda rather than a female Link. Personally, I find that idea more interesting, not to mention more "feminist". Why make a Ms. Male character when you have a female character perfectly capable of fullfilling the role? She'd need different powers, of course. A much stronger emphasis on magic than sword play. It'd be a nice change in pace for a series that could use one.

That said, for why people want a FEMALE Link, I'll just reiterate what others have said: they want choice. Unlike a lot of other established Nintendo characters, Link is meant to be an avatar for the player. You can even give him a different name in the game. If that's going to continue to be the case than the player should be able to CUSTOMIZE that character. Sex, hair color, and skin tone at the very least. White blond male Link can still be the face on the cover and in stuff like Smash Bros, but if Pokemon can do this, I don't see why Zelda can't.

I'm honestly not sure if I'd even make use of the option. For the last 5 years or so I changed my character to female whenever given the choice (aside from Skyrim, where I went with sickly, scrawny old man), for the sake of variety. But with women getting starring roles in more games I might go back to guys for a bit...

Now I can't get that image out of my head... :/

Zelda has a lot of girl fans and Link is a total blank slate character. It makes a lot of sense.

EDIT: It makes sense to ba a able to choose gender for the caracter.

I agree with your post as a whole, a female protagonist is just as believable as a male protagonist in a fantasy game I think. 

Now, there are some things I'd question with the bolded part. Would it be the same if Samus' gender could be customized? I think Samus, even more than Link, represents just a player avatar, with the exception that her name isn't customizable like in Zelda. Both in sidescrollers, since you just see the suit, and then in Prime games since it's first person. Now, there are some places where it would feel "different", like her death animation in 2D and her voice clips in 3D games. Also don't forget the later parts of Fusion where she is portrayed as very vulnerable (if people would think a male character in that situation would not feel as vulnerable it just goes against the point of equality, and I've read this point lots of times)

Would the crowd who wants female Link, feel the same about a male Samus?

There are historic reasons for samus being a lady (blowing the minds of ten tear old boys in the 80's who assumed she was male). Link is very effeminate as it is and it would be more like she finally came out as a women and had a party. I for one am happy for her.

Or they could make new main characters....

Isn't Link already androgynous enough?
If male Link gets a badass beard, I'm okay with female Links existence.

androgynous, not ambiguous. That's what she said. It's a completely different word and I think she's correct.

I agreed with Peer, the name Linkle is a bit crap but if it brings in more female players than i'm all for it, why shouldn't we be?

Link as he is, just is a boy ans should remain that way. There's been way too many games where there's talk about "the boy clad in green" and things to backtrack on that now. It also wouldn't make sense in the Link/Zelda relationship, and their relationships to the Triforce and how the reincarnation story in the series works. There just isn't a strong reason that doesn't boil down to "just because", to comply with such a change.

I definitely wouldn't be opposed to a spin-off game though where Zelda or Impa or someone new is the main character, could be fun. Or maybe even something in a main game like; Link and Linkle are twins, and at the start of the game you can pick one or the other and follow the story from their viewpoint (so have two 'paths').

However though, I've also seen talk here about customization. Just no. Play a different game, that's not what Zelda is about.