Why is Elizabeth so anxious to distrust Mr. Darcy and to trust Mr. Wickham?Please give me a full answer. I need it today.

Very interesting question. You may find it very useful to
know that originally Jane Austen wanted to call this novel First
Impressions, which obviously places far more emphasis on one of the key
themes of the novel - the extent to which we make judgements based on first impressions.
Another key element of the novel, as highlighted by the title we have now, is the
prejudice that Lizzie displays in her quickness to judge Mr. Darcy, and write him off as
an arrogant man.

Of course, the first sight we have of
Darcy is that of a very proud, disagreable man. In the assembly ball, he refuses to
dance with anyone except women of his "class", is harshly judgemental about the beauty
of Lizzie and so we, like the Bennets, agree with Mrs. Bennet´s assessment of the
man:

"...for
he is a most disagreeable, horrid man, not at all worth pleasing. So high and so
conceited that there was no enduring him! He walked here, and he walked there, fancying
himself so very great!"

Of
course, as Lizzie goes on to discover through the course of the novel, this exterior to
Darcy reveals the sensitive, caring, compassionate and honourable man underneath. But it
is important to see how the author is playing with us as she plays with her characters
in their assumptions. Mr. Wickham, when he is introduced, is featured as the exact
opposite of Mr. Darcy - they are foils of each other:

readability="9">

His appearance was greatly in his favour; he had
all the best part of beauty, a fine countenance, a good figure, and a very pleasing
address.

Thus we can see why
all the characters are so easily taken in by Mr. Wickham´s appearance, and because of
our first introduction to Mr Darcy we, like the characters, are more than willing to
believe Mr. Wickham´s fabricated account of how Darcy disinherited him. As Lizzie later
comments once she knows the truth of their
characters:

readability="6">

One has got all the goodness, and the other all
the appearance of it.

Of
course, the message is clear - Jane Austen is challenging us just as much as her
characters to not go by first impressions and to look deeper, witholding judgement until
we have more evidence. This is a lesson that Lizzie Bennet painfully learns, enabling
her to marry her true love by the end of the novel.