Vowels and consonants describe sounds. The sounds came first and the letters we call vowels and consonants came later as attempts to record them in writing. So the question should really be about why human speech has some sounds which come uninterrupted from the vocal cords (vowels), and why others are modified in the mouth (consonants). That is an interesting question, but not one that can be dealt with adequately in a few words. A short answer might be that human speech makes the best use of the bodily apparatus available.
English adopted the Roman alphabet and had to use its limited number of vowel letters to represent the English vowel sounds, of which there are around 20. A, E, I, O and U (and sometimes Y) have to be used both separately and in combination to cover the entire range.