Macduff's refusing to go to Macbeth's coronation is the first sign in the play that suggests that he is suspicious of Macbeth's actions. Somehow, Macduff is aware that Macbeth has not gotten his new titles through honest deeds, so Macduff decides to not go to the coronation--why should he honor a man who is likely false? Instead, Macduff says that he will return to his home in Fife, and shortly after that, he makes plans to go see Malcolm in England. So, with Macduff's refusal to attend the coronation, he shows disrespect to Macbeth as the new king, and an element of foreshadowing is put into place--Macduff eventually overtakes Macbeth and the crown is given to the rightful heir, Malcolm.
Macduff refuses to go to Macbeth's coronation, because Macduff is suspicious of Macbeth. Macduff is the only person to question why Macbeth killed the two guards. They are witnesses to the crime, and information could have been gotten from them. Macduff shows his suspicion by questioning Macbeth. Macduff knows something isn't right. Because Macduff is suspicious of how Macbeth attained the throne, he doesn't want to honor Macbeth at the coronation.
I also think that Macduff went back to his home in order to reduce his own danger from Macbeth. If Macbeth was willing to kill a king, then for sure he would be willing to kill Macduff just to keep him quiet. Macduff can't spread his suspicion around, if he is dead. Macduff knows that he is a potential target, so he leaves.
Macduff first becomes weary of Macbeth in Act II, scene iii, when Macbeth announces he has killed the guards. Earlier in the play, Macbeth and Lady Macbeth smear blood and leave bloody daggers by King Duncan's guards to frame the guards for King Duncan's murder. Macbeth says: "O, yet I do repent me of my fury, / That I did kill them," and Macduff's response is: "Wherefore did you so?" Macduff's response implies that he is initially suspicious -- why would Macbeth murder the only two witnesses available to explain what happened to the King? From this quote, the audience can derive that Macduff sees through Macbeth's lies. Macduff then decides he will "to Fife" (Fife is where Macduff is Thane) instead of Macbeth's coronation. He refuses to see Macbeth crowned as King of Scotland when Macduff believes Macbeth has been false.