I like the idea and could use the product, so I hope you continue working on it after the 24h. Of course, the tricky part will be getting enough traction that people can use the site as soon as they discover it. When I tried it, there was only one other person "searching" and apparently not my language combination.
I think this is great idea. I also think that promoting it on students' Facebook groups would be very effective. (I know that from my own experience- this concept has been implemented by my host university to help Erasmus students learn German/other languages and to help regular students learn whichever language they wanted. And I know the program has been having a great success. Lots of students were discussing on Facebook groups about this topic, trying to find tandem partners after the deadline set for signing up for the program. That's why I think you should take this approach to promoting this platform)
I really think this is a fun way of learning new languages, without all the blablas and grammar. Although usefull, I'm kind of like a kid who wants something here and now. The only difficulty from my point of view is bringing enough people online at the same time, at least until it is popular enough. Maybe some promoting (aka posting the link with a small description) on university groups? Just a thought.
Not directly topical, but I'd recommend changing the typography/whitespace usage of the landing page; it took me a few times where I needed to re-focus to read what it said.