Daria: I completed the CELTA in September, and I'm guessing their reason for rejecting you is that you really do need to have native or near-native English language skills. You need to be able to communicate fluently, particularly in terms of using the proper tenses within context, because the type of grammar and vocabulary that you will be expected to teach (verbally) spans a wide range. Being able to construct grammatically-correct sentences on paper is fine, but since you'll be speaking to these students, what you say and how you say will mean a lot. Judging from the grammar in your post, I can see why they suggested you take more time to improve your English. So do that, and then try again. Good luck.