Daf Yomi - Sukkah 37 - To Shake or not to Shake -That is the Question

The Mishna rules that we shake the lulav by ‘hodu’ and ‘ona Hashem.’ There is a debate between Bais Shammai and Bais Hillel if we shake by ‘hatzlicha no.’ The Gemora explains the significance of the shaking of the lulav and esrog. We bring it in front of us and behind to indicate that Hashem resides in all four directions. We shake it up and down to signify that the heavens and the earth belong to Hashem.

Does anyone have an explanation as to why Bais Hillel maintains that we shake the lulav by ‘hoshia no’ and not ‘hatzlicha no’?