Q: Why "half past" and not "half to"? When telling time and 30 minutes has gone past an hour, we say "half past". For instance, half past 4 or half past 5.
Why can't we also say "half to". For instance, half to 5 or half to 6?
Shouldn't it be a matter of preference, as it is when a glass is said to be half empty or half full?

A: The convention is that we express the time in terms of the hour that it's closest to. "A quarter past nine", not "three-quarters to ten"; but "twenty to ten", not "forty past nine".
"Half past" is, of course, exactly in the middle. The convention is that we say "half past" rather than "half to".
Sure, there would be nothing technically inaccurate about saying "half to". But as Barrie notes, the purpose of language is to convey meaning. If you don't follow standard conventions, it is more difficult for others to understand what you mean. I wouldn't say that you should never break the conventions. But I would say that you should only break the conventions when you have a specific reason to do so, like when you are trying to emphasize something or make a specific point.

A: If you make it a matter of personal preference you will defeat one of the purposes of language, which is to make your meaning clear to your listeners or readers. If no one else says half to, you may find that you will be asked to repeat what you have said in some other way. There is also a more direct risk of confusion. In British English, at least, half followed by an hour is used by some to mean half past [hour]. 
It's perhaps worth adding that in German, by contrast, half followed by an hour does mean 30 minutes before the hour named. Halb eins is not 'half past one', but 'half past twelve'. So there's no cognitive reason why time can't be expressed in this way.

A: For all other times on the clock, there are unique identifiers eg quarter past, twenty-five past, twenty-five to, etc. 
For half-past you could say half-to, but what would be the point? It means the same, and current accepted usage is half-past, so you might as well use that rather than use odd speech.

A: For the reason that anything that is half to is really half past the hour just preceding.  
It's probably considered better to state with reference to the past hour than the future hour in this case.  
This is just my conjecture, though.

A: I think it is a contraction, in the same way o'clock is.
When I learnt to tell the time, many years ago - Ponitous was still having flying lessons at the time...   I was taught: 
"One o'clock, Two o'clock to define the hour, when the long hand is on '12'.  It was explained that "o'clock" means: The time "of the clock" or as indicated by the clock.
Therefore, one of the clock simply means one hour indicated by, or of the clock's passage in time.
In the same way, "Half past" the hour is an abbreviation of the 18th or 19th century UK English idiom: "half of the hour past", that is you are half way through the last full hour of the clock, [as indicated by the clock].  Its worth remembering that, at this time [no pun intended], clocks and watches in general use were still relatively 'new technology'.
With time and use, "half of the hour past" was gradually shortened to become simply "half past...".
I seem to remember that in German, they refer to, for example, half past three [drei], as:

"halb vier" (half before four)

This may explain why I'm always late for appointments in Germany!
I am not certain of the reason for this fundamental difference, other than:


*

*German logical thinking

*The German sentence construction is significantly different to that used in English 


"Half of the hour past" is used here also:
The Holy Thief
Pengarron Land
