Why does mr Collins decide to introduce himself to mr darcy in Pride and Prejudice?

Answer 1

Darcy introduces his letter knowing that he has to tempt Elizabeth into reading his letter, knowing that she would not willingly read anything which to do on the matter of their previous interactions. Therefore, in starting the letter he addresses her in a very polite and civil manner, with the following of his immediate assurance that he will not renew his marriage proposal to her. He concludes his introduction paragraph with a compliment to Elizabeth, further encouraging her to read what he has to tell her by writing that she will read it not because of what she feels on the matter, but because of her justice. Here forth meaning that he is complimenting her on her judgment.

Following this introduction he attempts to explain to her why he took Bingley away from Jane when the likelihood of marriage was so great. Also he included the telling of his connection and encounters with Wickham in order to justify his behavior and actions towards the man, and clarify the untruthful tellings Wickham had so unjustly bestowed on Darcy. This is as well as to warn Elizabeth of his true character because he is aware of her past partiality towards the man and he wanted to clarify that Wickham had only the appearance of a good man, while Darcy had all the actual goodness himself.

Answer 2

Mr. Collins explains to Elizabeth when she attempts in vain to talk him out of introducing himself to Mr. Darcy that he considers "the clerical office as equal in point of dignity with the highest rank in the kingdom." He believes himself to be in part an equal to Darcy because he is a rector sponsored by Darcy's aunt. Also, during the Regency, if two people were introduced in a public environment it was required for them to acknowledge eachother afterwards forevermore, otherwise if one ignored the other he would be committing a social sin. Here Mr. Collins is forcing Darcy's hand in recognizing him, thereby elevating his status minimally in the public eye.