In photoshop they're mirror images are the middle of the pixel not the middle of the grid. So if I click on the nearest left side only one pixel shows because it's the middle part of the supposed symmetry. If the mirror was grid based than pixels, it will paint on both sides because minecraft textures are 2x2 in size.
I don't know for sure but I'd say if you've come across GIMP, MSPaint or other programs and look to their features (on the company website, reviews of the products or otherwise to see). Can't say much more as this isn't my area.
I did just come across this thread though, might be of some help. (Under the Pictures, Textures & Texturing spoiler).