Argentina-Chile road trip in December

I think that may be really ambitious for a first South American trip unless you're a true road warrior (and it helps to speak Spanish too because you will not find English spoken in out-of-the-way places, at least in Argentina). I would pick one country instead of zigzagging as your itinerary suggests. Don't underestimate the distances involved (as well as renting a car in one country and driving it to another - don't know what's allowed). I drove just in northwest Argentina (Salta area) through a mix of beautiful, empty and shifting landscapes, a wine route, and small Andean towns (the largest colonial city was Salta). I drove about 1,800-2,000 miles or so in 9 days. It was not hard driving, but still grueling. There were plenty of unpaved, small roads but no cars whatsoever (I was fined after returning the rental for damages from the gravel and wind damage to one door). I am really glad I could split the driving and not have to do it all. As wonderful and fun as it was, every day was incredibly long and tiring. I would not underestimate the distances and the empty land in South America. Also, you should find out about the condition of the roads just so you know what to expect. It was a road trip of a lifetime, but a LOT of driving. I rented a manual transmission.

Check out the Footprint Guides for both countries. Like I said, I would pick one but not both. The best use of a car is not to go to large cities like BA or Santiago, but to see the smaller ones and just the vastness of the landscape. That's why my trip was a combination of a road trip in the northwest, a few days just in BA and Salta, and 2 internal flights (one from BA to Salta and another from BA to Iguazu Falls). Don't assume that the weather will be the same even in summer given the differences in the regions like Tierra del Fuego and elsewhere.

Unfortunately a month is too short for the adventure you're planning. Also, there's nothing for 800 miles as you leave Buenos Aires, it's a very tedious and dangerous drive on 2-lane highways.
What would be doable in a month, is to combine a visit to Buenos Aires with a road trip to southern Patagonia only, for instance starting and ending in El Calafate or, more ambitiously, Bariloche (to both of which you can fly from Buenos Aires). And it will require serious planning, the right vehicle, authorization to cross into Chile with said vehicle (for Torres del Paine), reservations far in advance for accomodation in T. del Paine, and some contingency strategies (e.g. what if you get a flat tire 100 miles from the nearest settlement?). But it is one of the most beautiful regions I know in the world.

and some contingency strategies (e.g. what if you get a flat tire 100
miles from the nearest settlement?)

This is a really good point. There were so many times when we were literally in the middle of nowhere (imagine vast salt flats stretching to what looked like an infinite plane) and running slowing out of gas, not knowing where the next station will be. Planning for this trip was the hardest I've ever had to do because it was difficult to estimate driving times and not knowing where the provisions were (the guidebook was a good framework but there were so many holes to fill on the ground). If you reach upon some village and need something, you have to be prepared with good command of Spanish and you won't get the sorts of directions you'll expect (very imprecise, no street names, etc.) I have not been to Chile so I am speaking strictly of the Andean towns/villages in the northwest of Argentina. Still, it was a trip of a lifetime. I would do it again in a heartbeat.

Chile is much more manageable with better infrastructure, even on the Carretera Austral. However, by the nature of its shape it's hard to do a loop.
A month could easily see you land in Santiago, visit Valparaíso, take a short flight or bus to Temuco from where you drive south via the Lakes region (Conguillio National Park, Pucón, Puerto Varas...) towards Chiloé, then on to the Carretera Austral as far south as you dare, back north and across the Argentina border at one of several crossings, then on towards Esquel, Bariloche, San Martin de los Andes, and back to Temuco.
Visited most of these areas except Carretera Austral through a mix of self drive (in Chile) and buses (in Argentina) in 2013, on my own, without any trouble (but I am fluent in Spanish). The region doesn't have the same otherwordliness as southern Patagonia, but it was still unforgettably scenic.

I recommend taking a cruise around the horn from Buenos Aires to Chile or in reverse.
You would hit all the key ports, but avoid the lengthy land travel, which would involve some poor highways.
South America is wonderful, we especially love Peru, Chile and Argentina.

I think that may be really ambitious for a first South American trip unless you're a true road warrior (and it helps to speak Spanish too because you will not find English spoken in out-of-the-way places, at least in Argentina).

(e.g. what if you get a flat tire 100 miles from the nearest
settlement?).

Thanks for the warnings. We are indeed experienced road warriors, for example we drove from New England to the Arctic Circle (a village called Inuvik if you want to look it up) and Alaska, with part of the latter trip on one-lane gravel roads. We do speak passable Spanish and my husband has changed dozens of flat tires in his lifetime. We'll make sure we have tools and food on hand. There are rental companies that let you take a rental car from Argentina to Chile (with an extra fee for the necessary paperwork) or vice versa as long as you return it to the original country.

I did find some travelers last night on Trip Advisor who made a similar journey in our time frame or even just three weeks, so it doesn't seem to be unrealistic. An itinerary that does not include Tierra del Fuego is not worth the trip for us.

The cruise idea defeats the purpose of seeing the interior of these incredible countries, I don't think it would be a comparable experience if you're itching for a great road trip (away from masses of people). As for Tierra del Fuego, yes it's incredible, but I think people may also underestimate how incredible the other regions of Argentina are as well (and they're much less volatile weatherwise than Tierra del Fuego). The whole part of the northwest where I drove was magical (desert, cloud forest, mountains, salt flats, etc), although some of it resembled the Southwest in terms of scenery. Iguazu Falls was just incredible too, but no way would I spend more time to drive there and back - it required a separate flight.

Good luck with your planning!

Folks who took only three weeks to drive from Buenos Aires to Tierra del Fuego and back via Santiago? It sounds crazy, I'd really start no further north than Bariloche if I were to embark on such an epic journey all the way to Tierra del Fuego.
Otherwise, happy to see that you're experienced (way more than me!) and hope you'll report back with your route.