According to Brutus, why is it necessary that Caesar be killed? (Act 2, Scene 1)Shakespeare's Julius Caesar

In the "seduction scene" of Act I, Cassius lures Brutus
into thinking that Caesar perceives himself as a god, referring to Caesar ironically as
"immortal Caesar" and by strengthening his argument that Caesar has become too powerful
with allusion:

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Why, man, he doth bestride the narrow
world

Like a Colossus, and we petty
men

Walk under his huge legs and peep
about

To find ourselves dishonorable graves.
(I,ii,135-138)

Then, in Act
II, alone in his orchard, Brutus ponders the words of Cassius and the events of the day
in which Marc Antony has tried to put a crown upon Caesar's head, but ostentatiously
Caesar has refused it.  Brutus also considers that Caesar has slain Pompey, who was his
ally.  Persuaded by the arguments of Cassius that Caesar wishes to be emperor and sole
ruler of Rome, Brutus considers the assassination.  For the public good,
Brutus reasons, Caesar must be killed:

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Th' abuse of greatness is when it
disjoins

Remorse from power; and, to speak truth of
Caesar,

I have not known when his affections
swayed

More than his reason.  But 'tis a common
proof

That lowliness is young ambition's
ladder,

Whereto the climber upward turns his
face;

But when he once attains the upmost
round,

He then unto the ladder turns his
back

Looks in the clouds, scorning the base
degrees

By which he did ascend.  So Caesar
may;

Then lest he may, prevent.
(II,i,18-28)

Brutus reasons
that he has no personal reason to rebel against Caesar, but Caesar, who
has always been rational rather than emotional in his rule, may "climb the ladder" and,
once, in power, forget abandon humility as so many have done
before. Brutus fears that Caesar may
be

...a
serpent's egg

Which hatched, would as his king grow
mischievous,

And kill him in the shell.
(II,i,32-34)

That is, once he
attains such power as has been offered him by Marc Antony and the people, Caesar may
change and become tyrannical.  The idea that Rome "stand under one man's awe" (II,i,52)
is so disturbing to Brutus that he makes Rome a promise to "redress what will follow"
(II,i,57) and act for the good of Rome by preventing Caesar from becoming
a tyrant.