There was a similar thread earlier this month which I contributed to.

Your question seems to suppose there's an active academic debate about this topic there really isn't. There's a broad consensus around the 'Normanist' position. The 'anti-Normanists' were more or less limited to the Russian sphere. There has never been a single coherent anti-Normanist theory, but rather the various theory have tried to poke holes in the Normanist argument and substitute it with another theory of origin, which isn't necessarily Slavic either, the Khazars for instance have also been proposed. But to name some points and counter-points:

• Point: The Primary Chronicle of Nestor is not trustworthy.

• Counter-point: It is not read uncritically by scholars. As said in the previous thread, the idea that they'd be invited to rule people incapable of ruling themselves is not taken literally by most. But the very fact that such a 'founding myth' would be invented could in itself be taken as evidence that a justification for why a foreign dynasty were legitimate rulers.

• Point: There are no records of Slavs referring to Scandinavians as Rus'

• Counter: There aren't written accounts of any type from that era. But the Finnic names for Sweden (Rootsi/Ruotsi), derived from the coastal area around present-day Stockholm (today's Roslagen, the people there were Ros-Byggjar (Ros-inhabitants) or Rospiggar in today's language) demonstrate that this demonym was being used for Swedes by the neighboring peoples to the east early on.

• Point: Nestor writes the Rus' were known as such, "just as some are known as Swedes and others as Normans, English and Gotlanders." Therefore they cannot be Swedes.

• Counter: By the time Nestor was writing around 1100, Sweden had become a unified state with a single king and a single law for Swedes and the Swedish identity would've taken precedence over local sub-groups. Likewise, the concept of a single English people is a better match for Nestor's own time than for Rurik's. (see e.g.: this thread on that)

• Point: There's a Ros' (Рось) river not so far from Kiev, maybe they came from there.

• Counter: This is more of a thought than a theory, given that there's not really a coherent body of evidence around it.

• Point: It's to do with the Iranian Roxolani people who'd once lived in the Volga-Don area.

• Counter: That's even more far-fetched.

Some anti-normanist positions are built on straw-men, assuming more Scandinavian influence that thought and then not finding it. By all accounts the Rus' were integrated quickly; only two generations of rulers have names with Norse equivalents. (e.g. Rurik is from Rørek, Igor from Ingvar, Oleg/Olga from Helge/Helga) They were likely a fairly small group. Neither the original Rus' nor Varangians in general are thought to have been an ethnically homogenous group either.

As said in the other thread though, there is substantial evidence of Norse presence in the Rus' area and no dispute that the "route from the Varangians to the Greeks" (down Dniepr to Contantinople) was well-trafficed. You have both Byzantine and Norse sources on that, you have Norse names for the cities along the way (e.g. Holmgård for Veliky Novgorod) and even an account of the names of the rapids they needed to traverse along the way.

As I've said elsewhere, these travels eastward begin with the Viking Age (or some decades before it, given the Salme ship finds) when it's certainly an undisputed fact that the Scandinavians started traveling a lot more. Trading towns like Hedeby, Kaupang and Birka start arising in Scandinavia at the same time as Slavic ones like Novgorod and Wolin.

Anti-Normanism is in no small measure a nationalist reaction to perception of the 'Normanist' narrative as essentially being Scandinavians bringing civilization to the Slavs. While I'm sure that version of the narrative was probably held by some people in the 19th and early 20th century who believed in the inherent superiority of Germanic peoples, it's really got nothing to do with what the 'Normanist' history looks like now.

The image today is that of the Rus' being a small group of traders who arose as an small urban elite in these trading centers, which were probably quite diverse places with people and goods not just from the Norse but from the Wends and other Slavs, Finnic peoples, the Khazars, Byzantium and the Abbasid Caliphate. In that environment they assimilated partially to Slavic culture; they adopted the language, and would soon adopt Christianity as well; in short, it was a whole new culture that arose.