It IS possible: Select the image. Open effects (Window > Effects). Switch from "normal" to "multiply". Viola! White background is gone.
That only works with a white background. In addition, it introduces a transparency effect, with its associated problems.
With a rather light background: Select the image. Open clipping path (Object > Clipping Path > Options). Select Type > Detect Edges; use Threshold and Tolerance to get as close as possible to the edge of your image. This may be difficult because of a too low resolution image, or too much fringe on the edge -- if all fails, use the Inset Frame value to force the mask "into" the image. Click OK, and the background is gone.
But that's not the only way: you can always create a clipping path manually, and then you are in total control, not limited by transparency side effects, auto-edge detection, and busy backgrounds.