Yes ... avast is picking it up in the installer or the installation, either way Avast has an issue with p2p softwares. There may be a way of putting BS on the safe list of avast's safe lists for spyware, etc.
A number of security packages have adopted utilities that are not p2p friendly. I think that's the point File_Girl was making. BTW File_Girl is a programmer.

I suspect all Michwayne's link will do will confuse you. However if you find a fix then that's great.

The other option I can think of is you did not get Shareaza from the proper site as some other sites offer unofficial versions of Shareaza which have been tampered with.