The (Understandable) Arrogance and Audacity
The proposals of both Darcy and Crawford are similar in a significant way: their arrogance and audacity. However, it's also completely understandable. It's just math:
Gentry families have on average, 6.6 children in this era. Assuming your basic 50/50 split of boys and girls surviving the adulthood, you have your family of 3 girls and 3 boys. Boy 1 gets basically everything, Boy 2 goes into the army, Boy 3 goes into the church and etc. if more boys were born. Girls 1-3 hope they have sufficient dowries, great beauty, or they try for accomplishments. They also hope that Boy 1 isn't John Dashwood and decides that taking care of them when their father dies is just too troublesome.
Here is the problem when they want to pair off, there are 3 Girls and only one Boy 1, and he's the only one people want to marry. Mary Crawford wants a Boy 1, she violated the 1st Rule of Well-Dowered Women by falling for Boy 2 (Don't talk to second sons). So women have to settle for Boys 2 and 3 (and sometimes 4 and 5), and many go without marrying at all because of the men dying at war and at sea. But also because many of these Boy 2 and 3s don’t have enough money to actually marry on, they need or really want a Well-Dowered Woman.
Hence there are many spinsters and old, poorer bachelors and not that many choices for women to stay within this class. (and it seems like the main goal is not break class)
Darcy and Henry Crawford know the math, they know that basically any woman would be delighted to have a proposal from them, and they also think very highly of themselves. And let's face it, they are pretty solid catches, young, rich, and intelligent. So it makes total sense that they would go in to any proposal believing they would be accepted. This is why, "He spoke of apprehension and anxiety, but his countenance expressed real security." (P&P, emphasis the authors).
It is also why it takes an Elizabeth-level rant to disabuse Boy 1 of his pretenses.
(Quick note: Edward is the first born, but not a Boy 1 because his inheritance is not guaranteed. He also just doesn’t have the personality to be arrogant. Knightley, while also a solidly good guy, is the only Boy 1 we see propose to someone equal to him, not someone far below his “desserts”. And good old Bingles, we don’t actually hear his proposal, but he’s just too darn sweet to have audacity. Mr. Collins has the audacity even though he’s only a prospective Boy 1.)
