I found your problem!

You have to keep the image size at 100%!

(Sorry, I'm German! )

You can find this option at the bottom right of the "Save to web" dialog.

I think that's because of the GIF format's lacking transparency. It doesn't provide semi-transparent pixels. If you resize your image, it tries to keep all information correct, but to do that it wants to create semi-transparent pixels. To be able to save the image all the same it mattes the pixels with white.

Don't ask me why it's white or any other question. I don't know if it's true and I might have confused some terms whith the German ones but it's the most believable explanation I have!

The problem is that GIF cannot do partial transparency, which is needed for smooth edges.

If your intent is to put this on the web, try saving as a PNG-24 instead.

I suspect this is what's been the problem all along.

-Noel

Ah!  lol.  That's not a line at all.  You have what we call a "Poorly matted" graphic.  As previously indicated, because GIF can only support a single color being transparent, you'll have a very "jagged" edge.  This cannot be helped, because it's the limitation of the file format, and smooth edges actually employ very many color variations to be smooth.

GIF supports 1 bit of transparency.  That's 1 single color.

Try saving as PNG files.  They support 8 bits of transparency (2^8).  That's 256 different levels of transparency.  This will give your image a very sharp edge with no noticable matte.  But you seem new to PS, do you know how to create a PNG alpha channel?  This is what tells the file what areas of the image are see through and not.

Also, be mindful if you are viewing these images in IE browsers.  Older models are notorious for not supporting PNG transparency without having to do tweaks here and there.