Finding all pairs of numbers in a collection whose sum is some particular number
You haven't clarified what you're expecting your input to be but your code doesn't work unless the input is a set of positive integers starting at 1 and increasing 1 at a time.
For example:
var inputCollection = new List&lt;int&gt; { 5, 6, 7 };
var targetNumber = 12;

var pairs = ExtractPairs.Extract(inputCollection, targetNumber);

Clearly, 5 + 7 = 12 but your code returns no pairs! That's either a huge bug or the algorithm is expecting a very restricted input. I'd put my money on a huge bug.

Don't make structs with public mutable fields (unless you're in a very specific performance critical scenario). As pointed out in comments, I should have backed up this advice with some evidence. Here's an SO question about it or simply quoting the MS guidelines for struct design

X DO NOT define mutable value types.
Mutable value types have several problems. For example, when a property getter returns a value type, the caller receives a copy. Because the copy is created implicitly, developers might not be aware that they are mutating the copy, and not the original value. Also, some languages (dynamic languages, in particular) have problems using mutable value types because even local variables, when dereferenced, cause a copy to be made.

public struct Pair
{
    public int First;
    public int Second;
}

Make them readonly properties and add a constructor. I'd probably just use a Tuple&lt;int, int&gt; though.

Prefer formatting strings over concatenation:
Console.WriteLine(pair.First + &quot;, &quot; + pair.Second);

could be:
Console.WriteLine(&quot;{0}, {1}&quot;, pair.First, pair.Second);

In C#6 we also have string intperpolation:
Console.WriteLine($&quot;{pair.First}, {pair.Second}&quot;);

In this simple case, the concatenation is actually fine. It's clear because it's short. As things become longer and more complex, the format string approach can make the final string clearer to see for a human. There are also a great many options for things like padding and formatting numbers and dates that are easily done in the format string.
Just an FYI, the concatenation is turned into a call to string.Concat:
Console.WriteLine(string.Concat(new[] { pair.First, &quot;, &quot;, pair.Second }));