Sometimes its more important to spread a message across rather than throwing jargons around. Hence we have someone like stephen hawking explaining astrophysics stuffs to us in lay man terms.

I think the point of stating whether who is who is rather shallow compared to the reasons behind it.
No doubt everyone wants someone "great" in their history book and I supposed he should be the greatest behind it.

Main arguments :
1) Timeline : Islam civilization begins around 600 AD, Alexander is 300 BC, thats like a thousand year gap. I dont know how someone can write so much about someone about a thousand years ago.
For muslims, our history isnt start from our Prophet Muhammad, but it was already started from Adam. by time, in our belief,
our God sent a messenger (might be more) to a race. Thus, from our view, Alexander might be Zulkarnain.

2) Beliefs : Those are the days of paganism (even before Romans). Alexander liken himself to Achilles one of the heroes of Troy. It based on the greek mythologies, any islamic comparison ?
Facts can be altered through time. Since he alive in paganism era, the intellectuals in that time, will view him as paganism believer. 

3) Zulkarnain means 2 horns, Alexander is called by a similar name in Egypt as a reference to their gods too. But correct me that Egypt is under no Islamic influence during that period, they are worshipping Amun.
I got no idea about this.

4) Alexander is not really the "model" type. He pillage, murder, homosexual, hubris ........ etc. Not someone you want to be a prophet do you ?

Again, since he alive in paganism era, the intellectuals in that time, will view him as paganism believer.

BUT! This isnt make me say Alexander is Zulkarnain. Lot of Islamic Intellectuals writing on this matter, and alot of them arent agree Alexander is Zulkarnain. I have read some books that made by Muslims, they agree Alexander is Zulkarnain, but for me their writing is rely only on their theory, not facts. In Islam, theory with no support from our 2 main sources are cannot be accepted. my point of posting isnt to say either he is or not Zulkarnain, but more on explaining actual Islam. no offend please.

btw, today is 25 Dec. Happy Christmas Eve