A spineless person is said to be, "without moral force, resolution, or courage; feeble" - http://dictionary.reference.com/browse/spineless. So they are cowardly. But where did that term come from? Are creatures without spines such as worms or squids inherently without courage?
As Dan Bron's comment above suggests, there is a tradition (in English, at least) of associating such heroic virtues as standing tall, standing firm, and standing up for oneself (or for what is right) with having a backbone (that is, vertebrae or a spine).
Also traditionally, assuming the appropriate posture of a supplicant—whether on a battlefield or in a king's court or (metaphorically) in any other situation—involves bowing down or lying prostrate before the victor or superior person from whom the supplicant is seeking mercy or asking a favor.
It seems likely that someone long ago noticed that the posture of submission is one in which, physically, the spine plays very little role—and this insight, I imagine, encouraged the figurative relationship between spinelessness and lack of courage, fortitude, resolution, etc.
But this connection, I think, is strictly concerned with differences between perceived types of human beings—between those who metaphorically as well as in reality possess spines (and who, as a result, can stand upright on their own two feet) and those who metaphorically lack them (and who, as a result, cannot). I doubt that the figure of speech was influenced in any meaningful way by consideration of whether hornets, for example, are braver or more craven than field mice.