How does Hamlet's "To be or not to be" speech reveal his hesitation to kill Claudius?
Hamlet does not directly discuss killing Claudius in this soliloquy, which is more of a meditation on life and death in general. Hamlet reveals himself to be disillusioned with life, to the point that, if we could know about the hereafter with more certainty, death might even be preferable:
To die, to sleep—
No more—and by a sleep to say we end
The heartache, and the thousand natural shocks
That flesh is heir to. 'tis a consummation
Devoutly to be wish'd. To die, to sleep—
To sleep—perchance to dream. Ay, there's the rub!
So this soliloquy, while very famous, is, at least on the surface, irrelevant to his desire to avenge his father's death. Yet, as we see throughout the first three acts, Hamlet's reflective and sensitive nature slows him in his pursuit of revenge. He is not a man of action, but rather given to moments, like the one in this soliloquy, of pondering many of the fundamental dilemmas of the human condition, all of which seem to be playing out in front of his very eyes. Shakespeare offers his audience a trade. We are not gratified by seeing Claudius get his just deserts until the end of the play, and then only at the cost of Hamlet's own life. But by delaying vengeance, Shakespeare creates one of the most complex and fascinating characters in the history of English literature, and this soliloquy is a crucial moment in this process. It is a window into a tortured, sensitive, and brilliant mind.
I believe this soliloquy shows how uncommitted to killing Claudius Hamlet is. If he is able to consider dying and escaping his hardships, then he isn't seriously thinking of how to end Claudius. Hamlet considers suicide as a way to run away from his commitment. being uncomitted to his actions keeps Hamlet from falling through with his words of revenge and causes him to prolong and procrassinate.