We capitalise the first and the third letter because it is an abbreviation of the following:
- British English (BrE)
- American English (AmE)
I think (correct me if I am wrong, as I am also a learner of English) we capitalise English as it is the name of a language and languages always start with capital. This is why the abbreviations are the way they are.
PS: Hi everyone, I am new here! Nice to meet you :)