Taking the sentence as a whole, the texter feels that full disclosure is very important. Therefore, a text was issued. The text was issued in the spirit of the perceived requirement for full disclosure.
In other words, an act performed in the spirit of something is done because the something requires it. The reason given is often moral, as it is in the example.
hustle (v) : 2b. to sell something to or obtain something from (someone) by energetic and especially underhanded activity : SWINDLE
Your definition is close to correct, but this definition of the verb "hustle" always includes the suggestion of cheating someone in some way. For example, if I sell you a watch that I swear is a genuine Rolex, but which I know is actually a forgery, that's a kind of hustle. Or, if I pretend to fall down after being hit by your car, and try to get you to pay me money for my "injuries", that's another kind of hustle.
Or, as in the movie The Hustler, I pretend to be mediocre at a game in order to trick you into thinking you can easily win money from me, then, once you make large bets, I beat you and take your money. As you might expect, there is some risk with this scheme, as Paul Newman eventually gets his thumbs broken after hustling the wrong men.
Every city has its population of hustlers, and there are endless ways someone (or some group) can hustle their victims. These kind of schemes are not restricted to any particular country or culture. As previously mentioned, the plot of many movies involve some kind of hustle (The Sting, Matchstick Men, Dirty Rotten Scoundrels, The Producers, The Brothers Bloom, etc.) although in many of these it's not clear who is hustling whom.
However I would not use "hustle" on your teacher unless you really want to imply (playfully or otherwise) that he is trying to cheat you. Instead you want to use "brush me off".
Hey, that's not a complete answer and you know it. Are you just trying to brush me off?
Some dialects might also say "give me the brush". "Blow me off" is also common, but somewhat less polite.
Best Answer
Here is the full text of the letter:
The phrase in question, to breathe the air of human spirit once more, could be rewritten to say that the author wishes, once again, to do all of the things that make us human.
Friends, family, companionship, love, loss, joy, sorrow... it could be argued that it is the sum of these things that constitute the human spirit, and the writer wishes to experience them all once again. To savor them as you would savor the smell of a feast at a gathering of loved ones.
From the context of the letter, we can deduce that the author has done something which has rendered him an outcast, and he now feels less than human. The phrase "to breathe the air of...", in English, is commonly used as a metaphor for freedom, or escape, or of breaking free of a bond.
To answer the second part of your question, could it be rephrased as "to drink the wine of human spirit", I would argue that it does not work as well, since the spirit is an intangible thing, like the wind, and is more appropriately represented by the breathing metaphor.
Oddly, and to complicate the matter even further, the phrase "to drink the milk of human kindness" (Macbeth, Shakespeare, 1605) is well established in English.
Hope that helps.