Why did Banquo begin to hate Macbeth?

Rather than
hate, it's probably more accurate to say that, following the encounter with the three witches,is
deeply unsettled by their words and now needs to treat his fellow commander with all due
caution. Their cryptic divination, which foreseesas the next king and Banquo as the source of
the line of royal succession, would appear to set the two generals at odds with each
other.

First Witch

All hail, ! hail to thee, Thane of Glamis!

Second
Witch

All hail, Macbeth, hail to thee, Thane of
Cawdor!

Third Witch

All hail,
Macbeth, thou shalt be king here after! (Macbeth 1.3.50€“53)

To Banquo's request for a prophecy, they reply,

First Witch

Lesser
than Macbeth.

Second Witch

Not so happy, yet much happier.

Third
Witch

Thou shalt get kings, though thou be none:
So
all hail Macbeth, and Banquo. (Macbeth 1.3.68€“71)

Although both men are, at first, highly dubious about the claims of
these wild creatures, 's arrival with the news thathas named Macbeth the new Thane of Cawdor is
chilling. Once Duncan is murdered, without knowing for certain the identity of the assassin,
Banquo suspects that it is Macbeth, but still wonders whether this does not "set me up in
hope" (3.1.10).

In this briefand the succeeding scene in which Macbeth
invites Banquo to dinner after a day of riding, there is no sense that the general feels any
antipathy toward theas a possible killer or feels any concern for his own life at the new king's
hands. Thus, it is impossible to say that even in his final moments, he feels anything like hate
for Macbeth. In like manner, it seems clear that Macbeth has no feeling that could be described
as "hate" toward a man he simply feels must be eliminated. It's business, not
personal, so to speak.