My teacher is a Hindu nationalist who is doing a class on the Aryan Invasion, or more specifically on why it's wrong. He's quoting only Out of India theorists like Michel Danino or Koenraad Elst. That very biased lesson with an agenda left me very frustrated because I can't be sure how factual it was.
Can someone explain to me the merits and the weaknesses of those theories with a more academic approach?
You're talking about the origin of Indo-European speakers, yes?
http://web.vu.lt/rstc/a.pazeraite/files/2014/10/The-Quest-for-the-Origins-of-Vedic-Culture.doc
^ That links to Edwin Bryant's "The Quest for the Origins of Vedic Culture." Based on your question, this is by far the one I'd recommend the most.
I can't speak for his other work, but it's easy to become confused on the subject when just reading about others' opinions, and the supposed politicization or lack thereof from authors, whether European, South Asian, or other.
It does an exceptional job, in my opinion, of probing both sides and the current main body of evidence--without disproportionately doing a 'weighing both sides of the issues' (as political pundits might do on TV when promoting a highly discredited position).
It gives you a healthy appreciation for the popularly discussed pieces of evidence and leaves you with the understanding that our arguments rely on very little, and we actually know far less at the moment than some might have you believe. You should remain inquisitive and skeptic in your own right.
Archaeologically, there's a lot that will remain undiscovered and a lot of available work that just isn't even being done. Linguistically, we're still discovering things in terms of comparative research/reconstruction (Kassite deities' linguistic affiliations with Indo-Iranian or Indo-Aryan). In fact, a new indo-aryan language was discovered not that long ago, too, called Kholosi (in Iran) though it's history is unclear and might not yield any information on this topic. In the realm of genetics, if you read up on potential migrational history in the subcontinent via mitochondrial and paternal Y haplogroup DNA (like present R1a1a, or Tarim mummies having Indus Valley genetics), it becomes clear that human migration in general is exceptionally complicated and DNA stories leave us with tremendous mysteries.
Anyway, I think all this was to say that while evidence is skewed in certain directions, even that evidence's significant blind spots should be thoroughly understood in order to grasp the nature of such problem-solving. It may not be a matter of "were these people Munda, or Dravidian?," but even more relatively recent populations are profoundly mysterious in the nuances of their origin.