Why does Hamlet suspect "The spirit I have seen may be devil," when he assured Horatio that "It is an honest ghost"?In Shakespeare's Hamlet

In Shakespeare's Hamlet, the
supernatural is a major element of the story.

Shakespeare
is writing to an Elizabethan audience that has been born into the belief of the power of
the supernatural, and fed a diet of tales of what the "other-worldly" are capable of
doing.

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...Elizabethans truly believe in the existence
of these spirits...they even have somewhat of a list as to the characteristics of
ghosts. These characteristics are embedded within Shakespeare’s writings and are
followed to exactness. The first and foremost characteristic is that ghosts
are considered evil spirits that impersonate the deceased. This
characteristic helps to provide a plot such as in Hamlet where when
the father’s ghost first appears, Hamlet does not know whether he is good or evil.
Therefore, when the ghost seeks out Hamlet to do his bidding, Hamlet does not know if he
should follow the apparition’s
bidding.

I think
that seeing the ghost goes a long way to convincing Hamlet that the
ghost is an "honest" one at that moment. This may be why Hamlet
initially tells Horatio that he believes the apparition. However, when the night is over
and daylight returns, so does reason. Hamlet (a personification of a character with
Elizabethan viewpoints) will think twice about what he saw the evening before. Being
concerned over the Ghost's "credibility" would be the result of Hamlet's common sense
challenging what Hamlet had witnessed under a cover of mystery and darkness the night
before.

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Hamlet, especially,
provides the common perception of a ghost. This apparition is seen as a tormented figure
who suffers purgatory because of his murder and wife’s adultery. And to reiterate the
common beliefs, Hamlet is torn between thinking of the ghost as his father in life and
experiencing and seeing the actual disturbing apparition. When ghosts are not actually
seen...when it involves the imagination of the character, the audience still perceives
the effects of the apparition as it seeks to persuade a human to enact revenge. This is
due to the widely accepted belief that a ghost does not have its own powers but must use
the power of persuasion to exact revenge. Shakespeare uses this perception to develop a
sense of doubt and eventually forces a revelation upon the audience. This pagan element
is accepted in its entirety by the audience as a true possibility. The use of ghosts
within Shakespeare’s works is both entertaining and believable since its actual
conception is derived from society’s beliefs.
(www.writing.com)

Because the
Elizabethan audience believed unequivocally in the power of ghosts to appear after
death, there would have been no doubt that Hamlet indeed saw a ghost. Old Hamlet's ghost
did not have the power to make Hamlet exact revenge: Hamlet had to agree of his own free
will. However, the audience would still harbor doubts as to the identity of the ghost:
is it, in fact, Hamlet's father? Elizabethans believed a ghost could be evil, pretending
to be a lost loved one, thereby tricking a living person to do its bidding (most of the
time exacting revenge).

Because the Prince has so much to
lose if he aligns himself with an evil spirit, he must be certain
that he is dealing with his father's ghost. This is why he hesitates so long in acting
against Claudius, even though his heart tells him it's true; once Claudius reveals his
guilt at the play, Hamlet has the proof he
needs.

Additional
Source:

http://www.elizabethan-era.org.uk/elizabethan-ghosts.htm