In high school, we were taught that a paragraph begins with a topic sentence--a sentence that states the main point of the paragraph--and follows with evidence supporting the topic sentence.
It is true that many paragraphs are like that. But it is equally true that many are not. When it comes to writing in the real world, paragraphs can take a number of forms.
An excellent discussion of the forms a paragraph can take is found in George Gopen's Expectations: Teaching Writing from the Reader's Perspective. Gopen, a professor of rhetoric at Duke University, says that paragraphs are best understood as consisting of three parts: an issue, a point, and a discussion.
The issue puts the point of the paragraph in context. The point is the old-fashioned topic sentence. The discussion is an elaboration of the point.
Here's an example of a paragraph with an issue, point, and discussion. It appears in Malcolm Gladwell's 2000 book The Tipping Point:
A book, I was taught long ago in English class, is a living and breathing document that grows richer with each new reading. But I never quite believed that until I wrote The Tipping Point. I wrote my book without any clear expectation of who would read it, or what, if anything, it would be useful for. It seemed presumptuous to think otherwise. But in the year since its publication, I have been inundated with the comments of readers. . . .
Here, the main point--that Gladwell did not learn something in particular until he wrote his book--is stated in not the first, as my high school teacher might have wanted, but in the second sentence. The first sentence instead introduces what Gopen would call the issue: the context in which the point is made. The rest of the paragraph goes on to discuss the point, documenting the interplay between Gladwell and his readers and how it has changed his understanding of his book.
Here is another example, with a longer issue and the point coming later in the paragraph. It's from Thinking, Fast and Slow, the 2011 book by the psychologist Daniel Kahneman:
When you are asked what you are thinking about, you can normally answer. You believe you know what goes on in your mind, which often consists of one conscious thought leading in an orderly way to another. But that is not the only way the mind works, nor indeed is that the typical way. Most impressions and thoughts arise in your experience without you knowing how they got there. . . .
Here, the main point is stated in the third sentence: But that is not the only way . . . The first two lay out the issue, providing context for the point.
Take a look at your paragraphs. Do they all begin with a topic sentence? Or do some of them begin instead with an issue before stating the main point?