Something that's defensible is excusable — you can defend it or justify it. Mistaking your friend for her twin sister, as awkward as it may be, is a defensible blunder.
In politics, there are often issues to which some people object strongly, while others argue that they're completely defensible positions. You may believe it's defensible to wage war in some circumstances, while your pacifist friend thinks it's never okay to kill for any reason. Defensible comes from an Old French root, defendre, "defend or resist," from the Latin root defendere, "guard or protect."