This is just a peculiarity of British English that read can have this particular meaning. The New Oxford American Dictionary says:
3. chiefly Brit. study (an academic subject) at a university: I'm reading English at Cambridge
[ no obj. ]: he went to Manchester to read for a BA in Economics.
So, it's more about language itself than the official title of the diploma or an academic custom.
— Hey, wait, but where does this idea come up to associate “read” with “learn, understand”? Surely there is a reason? And why is it English only?
Well, as it turns out, the meaning of “learn, understand, think, explain” is actually the original meaning of the Old English word from which we inherited read! The Old English word is rædan (“explain”, amongst its meanings), from Proto-Germanic raedanan, from Proto-Indo-European root re(i)- (“to reason, count”).
Now, in many languages, the words derived from this root kept their original meaning. In German, raten means “to advise, counsel”; in Icelandic, ráða means “advise, decide, solve”.
Now, at some point something in Old English went sideways. Wiktionary states very clearly:
The development from “advise, interpret” to “interpret letters, read” is unique to English
Etymonline is more specific:
Transference to “understand the meaning of written symbols” is unique to Old English and (perhaps under English influence) Old Norse raða. Most languages use a word rooted in the idea of "gather up" as their word for "read" (cf. French lire, from Latin legere).
Now, the original meaning of the word read is retained in some contexts in British English, but was lost in other forms of the English language, such as American English.
As a summary, the hard question is not really “why can read mean study”, but instead: why did read come to mean “read”?
(source for the above: my memory, which is backed by the most excellent Etymonline)