My son is a bully

It's terrible.  My dear son Aiden is a bully.  Most of the people who know about his behavior would tell me that it is "better for him to be the bully than the bullied".  While I do agree to a certain extent that it is better, it is still unacceptable behavior to me!

From the first day Aiden exhibited such tendencies, we have been telling/explaining to him why bullying is naughty/unacceptable behavior and that it hurts the victim.  And he understands - he would listen and nod his head, before faking a beating action followed by shaking his head and waving his hands to indicate that it is not acceptable.  Most of the time, he would also offer his apologies to the victim.  We also noticed that he would only bully certain people.  To other kids, he would be very friendly and sometimes even shower too much love (think random handshakes, hugs and kisses).

Last month, his teacher in Playgroup told us that he fought a girl in class over toys and even bit her!  A few weeks ago, while playing with the water jets at the pool, he gave his trademark naughty look before shoving his playmate Levine in the back intentionally and unprovoked.

Aiden the bully.

I have never beaten him and Cheryl has already stopped using physical means to discipline him.  What is wrong and how can we correct this?