In Act III why does Macbeth keep his attack on Banquo a secret from Lady Macbeth?
Secret? No, Macbeth does not keep the imminent murder of Banquo a secret. He does more than suggest what he plans to do in relation to Banquo and Fleance; he just leaves the specifics as a little surprise for his wife. It's as if Macbeth is using murder as a present for his wife which she will thank him for after she opens the package. Actually, Lady Macbeth, in this little exchange, suggests the murder first (Act 3, scene 2):
O, full of scorpions is my mind, dear wife!
Thou know'st that Banquo and his Fleance lives.
But in them nature's copy's not eterne.
There's comfort yet; they are assailable.
Then be thou jocund. Ere the bat hath flown
His cloister'd flight; ere to black Hecate's summons
The shard-borne beetle with his drowsy hums
Hath rung night's yawning peal, there shall be done
A deed of dreadful note.
What's to be done?
Be innocent of the knowledge, dearest chuck,
Till thou applaud the deed.
You see, he just wants her to wait a bit, innocent only in the details. The two of them make a sick, murdering couple, don't they? The irony is that, at the big dinner they are throwing this night, she will learn only to well what has happened to Banquo and his son Fleance.
Macbeth does not tell Lady Macbeth the details of his planned attack upon Banquo because he feels that it is better that she not know until the deed is done. Afterwards, Macbeth adds, then she can "applaud the deed" (3.2.46).
Macbeth also tells Lady Macbeth not to question him yet about his plan of action as he does not fully know what will happen because "Things bad begun make strong themselves by ill" (3.2.57). That is, once begun, bad deeds often lead to others.
Scene 2 of Act III is replete with imagery of turmoil and suspicion as Macbeth's hands sink farther into blood. Aware of the witches' prediction that Banquo's sons will be kings, Macbeth fears that his slaying of Duncan will not profit him if Banquo lives, for there will still be threats to his hold on the throne since the witches have said that Banquo's sons will be kings.
Perhaps, then, Macbeth refrains from telling Lady Macbeth too much because he does not want her to know that he has instructed the murderers to "leave no rubs" (3.1.134) and kill not just Banquo, but Banquo's son Fleance as well.