Why not the group?

Have a read about kin selection, for instance. There are lots of facts about e.g social insects (like the male/female/sterile ratio iirc) that were thought to only be explainable by group selection, but later were found to work out purely from considerations of gene selection. I'm just a layperson though, would highly recommend Dawkins writing on this stuff. It's much less polemic than his writing on religion, if that puts you off at all.

I think the basic criticism of group selection is that at an individual level it can be beneficial to go against the group's goal, and you need to explain why that doesn't happen (even very small advantages are rapidly boosted by selection). This is one of the great puzzles of selection - how does cooperation evolve from selfish interests? The theory of group selection just asserts that it does, which is not very satisfactory.

There's behaviour at an individual/group level that is only explained by selection at a lower level. Consider the placenta releasing allocrine hormones during pregnancy while the mother's body increases insulin levels, or consider male lions killing off the cubs of defeated males.

Group selection only works under some rare situations. Groups should rapidly build and disintegrate to make group selection work.