For me I'm not so sure it's a matter of being pushed towards the Left as it is backing away from the Extreme Right (as well as religion). I identify more with "center-left" (economic rationalist/pragmatist) parties because they don't tend to have (or have less) religious fundamentalists, racists, homophobes, xenophobes, sexists, anti-intellectuals, creationists, reactionaries, and social conservatives. Other factors were increasing wealth and income inequality, concern for labor and the social safety net, and general economic f[Inks]ery of the Right.
Also:
moderates like Bob Dole and George HW Bush
Dole and Bush weren't moderates, they were solid conservatives.
