Before we can answer about Mr. Collins, we have to sort the assumptions in this question out a little bit. First, consider that in the 1700s and 1800s it was not uncommon for cousins to marry to keep property within families and because of attraction resulting from lifelong familiarity between families. Secondly, consider that Mr. Collins gives no indication at all that he might "feel he needs" to marry one of his cousins. On the contrary, he expresses the opinion that he is quite excited about his idea and about the fact that his patroness, "the Right Honourable Lady Catherine de Bourgh, widow of Sir Lewis de Bourgh," deigns to give approval to his plan.
I flatter myself that my present overtures of good-will are highly commendable, and that the circumstance of my being next in the entail of Longbourn estate will be kindly overlooked on your side, and not lead you to reject the offered olive branch.
So the question at hand really is: Why does Mr. Collins wish to propse to one of the Bennet girls? This question is even more interesting because he starts his letter of introduction to Mr. Bennet by saying that he hesitates to make amends with Mr. Bennet and his family because his father, the deceased Mr. Collins, was to his dying day ill disposed (swimming in dislike) toward Mr. Bennet.
I was kept back by my own doubts, fearing lest it might seem disrespectful to his memory for me to be on good terms with any one with whom it had always pleased him to be at variance.
First: Mr. Collins wishes to marry one of the Bennet girls for a fourfold reason.
- He is a clergyman and believes he should set the example of marriage for his parishioners.
- He wants a wife right away because of his new position as pastor of Lady de Bourgh's parish church.
- He is the one to whom the Bennet's Longbourne estate will devolve upon Mr. Bennet's death due to the entail.
- He recognizes the double benefit a marriage to one of his cousins would give Mrs. Bennet and her daughters: a daughter married and future security.
This list of reasons leads naturally the follow-up question that you ask: What does Mr. Collins hope his proposal will accomplish? The answer to this springs from--or more correctly grew from--the reasons stated above for his desiring to marry a cousin.
Second: Mr. Collins knows that a successful proposal of marriage to one of his five cousins will accomplish the happy effect of continuing to provide all six women (Mrs. Bennet and her five daughters) with a home for as long as they each should need it. The consequence of an estate being legally entailed away from the female line of a family is that when the nearest related male to the estate holder is in another branch of the family (i.e., the Collins branch), then the estate goes to the other branch.
What this would result in for the Bennets is that as soon after Mr. Bennet's death as Mr. Collins (and his wife) might wish to do so, they could (and probably would) remove the Bennet women from Longbourne and render them homeless. With their limited inheritances, this would reduce them sorely in circumstances. To understand these concepts, think of how Mrs. Dashwood, Eleanor and Marianne were cast from thier home by their half brother John and his ungracious wife in Sense and Sensibility and of the lowly state that Miss and Mrs. Bates were living in when Mr. Knightley describes them as being fallen from a higher financial and social strata in Emma.