You know, in Buenos Aires it's so easy to get a job.....as an english speaker...
I still get regular job offers through agencies from there......there are SO many companies who will hire you and need you just because you are a native English speaker. My experience with teaching english here back in the day was that it was more trouble than it was worth. BUT...you need to get good at speaking spanish as well....a point that all too often to many ex-pats overlook unforutnately. You also need to make lot's of friends and connections. Don't underestimate the power of networking here...ALOT of opportunities will come through "who you know" in Argentina.
Back in the day I went to one English teaching "institute" and they wanted me to offer a course on speaking english and teaching american style slang etc. But the problem was ( of course ) they wanted to pay me all in "negro" ( work under the table, way below minimum and without declaring earnings to the gov't, no paid holidays, bonuses nothing ) and WAAAY below the minimum salary "sueldo minimo" like barely $1000 pesos a month.... you can't even pay a fraction of your rent with that LOL! Even the guys sweeping trash off of the streets here get at least $5,000 - $7,000 pesos a month ( that's minimum in BA now right..I'm not sure? ) and bonuses and all the legal benefits that by law you are supposed to receive.
Jobs, employment anything business related here, you need to be assertive and not passive because they'll walk all over you....I mean it. It's always sketchy and they'll jerk you around if given the chance, ( especially trabajo en negro ) even if it's just a few little details or out of a few pesos..... they'll get you somewhere...it's the way things roll here and argentines know how to deal with it. So, I said no way and never looked back. Needless to say the English institute closed about a year later... Look, in Argentina, something like 35 - 40% of all employment here in Argentina is in "negro" it's a nightmare, so you need to be aware of that. ALOT of this kind of work, teaching in English, it's going to be usually very low pay, no benefits and in "negro" it's unfortunate but the way it is. You'll even be lucky some months if you get paid on time, let alone "at all". I know this because of my own experiences and other expats I know who went through the same thing. This is just the reality here...
If they see a foreigner coming who doesn't know the language or the "lay of the land" "rules on the street" here....you're gonna get hosed. Employment is a touchy issue here...usually problematic at best...good companies are harder and harder to find.
So, later, I tried advertising and teaching from home, here theres no accountability and little responsibility. This was even worse, half the time people could only pay me half, or told me "I can't pay you this lesson but I'll pay you the next one" ........of course I never got paid, or I didn't get paid until a month later, usually only after calling or hounding them to bring me the money. The classes I scheduled at months end were the worst... ALWAYS issues. Students constantly came late or called to cancel or reschedule, usually last minute.....it was a nightmare, I did it for a few months and said that was it.
Then my spanish begin to really improve ( thanks to my wife and family ) and I quickly discovered how easy it was to offer my services in english to alot of decent companies looking for and needing native english speakers, and all trabajo en "blanco" ( fair salary, declared to the gov't, taxes paid as well as paid holidays etc.. ) some of it even working from home. So I found that and I never looked back. I would recommend NOT teaching english, at least not to make a living, it's just too much trouble here and it doesn't pay....I'm sorry to break it to you but it's the honest truth.