I'm sure Sharon thinks of it as facing the Future, with all the marxist implications that entails. Onward to Utopia.
You clearly do not know the Prime Minister or his history. He is a centrist or a moderate. Always has been, always was, even back when he was with the Liberal Party (merged into Likud) or his own Shlomtzion party.
Also, don't assume American political terminology (i.e.: that forward somehow equals progressive) applies in Hebrew. The only reason for the name change is that Aharayut Leumit was a mouthful.