My student is asking "why must I say 'it makes it hard to..'"

The word 'angry' is describing him - it makes him angry (or me, or you, etc.).

The word 'hard' is describing an effect from something external, such as air pollution or asthma. 'it makes it hard to breathe sometimes'.

By the way, using the phrase 'it makes me hard to breathe' is slang for your student getting an erection from breathing. This is one error that really doesn't mean what he thinks it does.

Native speakers use these grammatical forms as idioms. We don't think about the grammar. But it seems to me the pattern is pretty consistent.

It makes object noun or pronoun adjective optional prepositional phrase

It makes it bigger.
It makes me happy.
It makes it difficult.
It makes her sad to see me go.

Jespah is right. The phrase "it makes me hard" is sexual. American speakers will see this as referring to being sexually aroused.

It makes me hard when I hear the opening Star Wars theme... (possibly TMI).

I think some German speakers in the 1940s saw it differently.

Good quote Centrox. That use of the word "hard", meaning tough or unmoveable, seems archaic to me as a modern American speaker. But this quote is perfectly understandable in this context.

Maybe it's a UK-US thing. If I am in a pub, and a bounder gets obnoxious to the ladies I am with, and I say "Pipe down, there's a good chap", and he (foolishly) squares up to me and says "Come on if you think you're hard enough", so that I have to teach him a lesson, I know exactly which "hard" he means, and it is not at all archaic. I know Mae West is supposed to have said "A hard man is good to find". The first meaning in one's mind when told about a "hard guy" is that he has tattoos, wears a wife-beater vest, and is not shy about punching guys out who challenge him. Not a fellow with a boner. Sometimes called a "hard nut".

In the Northeastern US (at least in the circles in which I travel) we don't use "hard guy" this way.

Heh, "come on if you think you're hard enough" would elicit snickers from the bargoers here. The erection connotation would be the first thing coming to mind.

Complete with your/you're confusion...

Apparently the British "hard" causes transatlantic merriment...