Why would the hydrophobic part arrange itself toward the center of the cell membrane?

Hydrocarbon molecules are strongly hydrophobic ("water fearing"), and it is this strongly hydrophobic layer of material that gives the cell membrane its "water proof" nature and allows it to act as a container for the cell and its contents. It would be useless to make a container of something that easily dissolved in water!

Proteins associated with a cell membrane, therefore, must be able to interact with both an aqueous, hydrophilic environment, and with the lipid, hydrophobic environment of the inner parts of the membrane.

Explanation:

Hope that helps:)