In Cantonese, 唔知邊個打邊個 means "don't know (confused) who is who"
The verb 打 (hit; attack) here seemingly occupy the position of 'is' in this phrase
But the meaning of 'is' is not included in the 打 entry in dictionaries
So what is the role of 打 in this expression exactly?
“打” here means 對 / 配對。instead of “is”, it should be better translated as “matches” or “associate with”.
Other examples: 打成一片。 猜謎。打一物。
My understanding, or the way I remember it, is that "打" (da) is the "lazy" pronunciation of "搭" (daap), without the 'p' sound. 搭 usually means "matching" like in 搭配, so the expression would literally mean "don't know which matches with what".
My theory is, 打 in 唔知邊個打邊個 should be interpreted literally as 'hit/attack/fight'. The whole phrase means "don't know who fights who" and "can't tell who is who" is an extended meaning.
There are many expressions we use today were from Chinese opera. Imagine watching a group fight on stage, everyone is fighting with everyone else. The audience might get confused and can't tell who is fighting who.
This expression sounds to me more likely to be used when someone watches a group/team fights/plays against another one, and the person doesn't know the name of the two groups/teams.
For example, 今日又場球賽，但我唔知邊個打邊個。
唔知邊個打邊個
As you well know, this is a common Cantonese colloquial phrase which Mandarin speakers will have a hard time appreciating.
We use it all the time to express a situation where there is confusion / disorder / a melee of riotous activities. An English equivalent would be something like "pandemonium" or "chaotic", not necessarily in the context of a sporting contest, but includes a shouting match of people quarreling.
So, the extended meaning of 打 here would include "against", "versus", "oppose"
Confining it to just the physical meaning of "hit" or "beat", do not do justice to this really colorful and useful phrase. I always keep it handy when I have no good answer to any embarrassing situation or wanting to politely get rid of a pesky busybody.
I am not conversant with any historical, literary usage, but in the context of everyday Cantonese usage, interpreting it as "is" is odd, because the whole phrase is not about "who is who", but who is doing what to whom, hence 打, (hit or beat)
My knowledge of Cantonese at the best of times is limited to the "rough", colloquial variety, so please take my answer in that spirit.
