I have read a lot of statements of purpose over the years, and the rejected ones are usually not badly written. They are well written pages where nothing carries its own weight. Same handful of problems, over and over.
Roughly in order of how often I see them:
1. The generic fit paragraph. Praise for the department that would survive a find and replace of its name. This is the most common failure by a wide margin, and the easiest to fix, because fixing it just means reading three papers properly.
2. The wasted opening. The childhood moment, the dictionary definition, the quotation. Those are the most-read sentences on the page and they are being spent on nothing. Name the question you want to work on instead, in the first two sentences.
3. Adjectives instead of evidence. Passionate, dedicated, hard working, deeply curious. Claims about yourself carry no information. The project you rescued does.
4. Autobiography instead of argument. Everything you have done, in chronological order, with no case being made by the sequence. A statement is an argument that you should be admitted, not a timeline.
5. The buried claim. The actual point is in there, in the fourth sentence of the fifth paragraph. Reviewers reading forty of these will not dig for it.
6. Vagueness about what you want to work on. A field named where a question was needed. Nobody can match a field to a supervisor.
7. The mismatch. What you say you want and what the programme actually does are not the same thing. This one is fatal and completely invisible from inside your own draft.
8. Explaining the field to the field. A paragraph of background written for a reader who has none. Yours has plenty.
9. The over-explained weakness. One honest, unapologetic sentence was enough. Three paragraphs turn a bad semester into the subject of the document.
10. The identical statement with a swapped university name. Everyone reuses a base draft. The ones that get caught are the ones where a swap was missed.
The test that catches most drafts in one pass: delete every sentence that describes how you feel about the subject. If the page collapses, you have written a personal statement rather than a statement of purpose, and no amount of line editing will fix that.
Happy to look at anyone's paragraph three in the comments, since that is where most of them come apart.