Your question relates to a difference between the various forms of English spoken around the world. In most varieties of English, the alphabet refers to the collection of letters used by a writing system:
A set of letters or symbols in a fixed order used to represent the basic set of speech sounds of a language, especially the set of letters from A to Z. - Oxford Dictionaries
For example, the Latin alphabet as used in English is:
and the Cyrillic alphabet as used in Russian is:
In the debate you had with your friend, you were using the word alphabet to refer to an individual letter, rather than the collection of letters.
This is a common and correct usage in Indian English (and perhaps some other varieties), but would be considered wrong (and may cause some confusion) in British or American English.