Excellent questions... (I like your approach on this thread, btw.)
I guess what I meant by "offended" is that often the Gospels tell us something that runs counter to our own beliefs and behavior. In response we become defensive in some way; we might try to argue past the difference, and can offer all sorts of good reasons for why our case is different, and the Gospels really don't apply.
That defensiveness takes any number of outward forms -- whether it be anger, apathy, or branching off to form a new religion. But in any case, we're at odds with the Gospel -- it "offends" us.
Is everybody who hears the Gospel offended by it? No, of course not. Should they be? Probably.
Which Gospel?
"For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth..."(Romans 1:16). What is the gospel of Christ?
"That if thou shalt confess with thy mouth the Lord Jesus and shalt believe in thine heart that God hath raised Him from the dead, thou shalt be saved".(Romans 10:9) "For whosoever shall call upon the name of the Lord shall be saved." (Romans 10:13).
Is this part of the Gospel of the Kingdom?