First you must keep in mind that Scone is the place where the king's coronation takes place. This is tradition, and it is expected that all who are loyal to the king will be there for this important ceremony. When MacDuff does not attend Macbeth's coronation (or official crowning ceremony) it raises red flags for Macbeth, and it shows us that he is not a supporter of the new king. MacDuff doubts Macbeth's position as king. He is the first to express concern that maybe Macbeth had something to so with Duncan's untimely death. This, coupled with the witches' warning, put MacDuff on Macbeth's radar as he looks for ways to eliminate anyone who may be in his way to keeping the crown.
By not being present at Scone for Macbeth's coronation, Macduff shows both distrust of Macbeth and disrespect towards him. He believes that Macbeth has not inherited the throne rightfully, and it is implied that he believes that Macbeth has resorted to some wrong and desperate measures in order to become the new king.
In Act 2, Scene 3, when Macbeth kills the guards, Macduff is the first to question Macbeth's action:
MACBETHO, yet I do repent me of my fury,MACDUFF
That I did kill them.Wherefore did you so?
He asks Macbeth why he killed the guards, probably thinking they could have given some important details in relation to king Duncan's murder. He wonders why Macbeth eliminates them in such haste. Macduff's reaction is an indication that he believes something is wrong and that Macbeth is not innocent in the entire affair. For that very reason, he chooses not to be present during Macbeth's coronation, and he turns out to be Macbeth's greatest rival, as the play progresses. His refusal to join the celebration in Macbeth's honor only foreshadows that things will not go smoothly for Macbeth as the new leader of the country.