The main reason would be that Nestor's Primary Chronicle says as much; that there were a group of Varangians (vikings) called the Rus, who were supposedly invited to come and rule the peoples there.

The rest is largely circumstantial. It's well established that the Vikings/Varyags were trading and travelling through there and down the Volga. The theory is that the name 'Rus' would refer to Roden in Sweden, whose inhabitants were known as rosbyggiar ('Rospiggar' in modern Swedish). This is the coastal area closest to Finland, and it's known from things like runestones that the inhabitants there made Viking trips to the east. This toponym/demonym also gave rise to the Finnic names for Sweden (Finnish Ruotsi, Estonian Rootsi) as a pars pro toto. (And conversely, Finland Proper is the region on the opposite coastline, closest to Sweden) Another circumstance is that the earliest Rus' rulers had Old Norse names, or at least names with Norse equivalents. Rurik to Rørek, Igor to Ingvar.

Even if the Normanist theory is taken to be true, they would not have formed more than a small ruling elite, and were by any account quickly assimilated - Rurik's grandson was named Sviatoslav - a distinctly Slavic name. So it is not at odds with the fact that they're culturally, ethnically and linguistically distinct. So are the inhabitants of Normandy, but there's no dispute over them having been ruled by another small elite of people of Scandinavian origin. There was a some influence of course, but the Norman people were always much more French/Frankish than Scandinavian/Norse.

Anti-Normanist theories have tended to focus on the implausibility of Scandinavians being invited to rule these Slavs who, according to the account, were incapable of ruling themselves. It's hardly a flattering story, and does seem rather unlikely - but on the other hand, that part could be false without rendering their geographic origin false. (If the Rus' had come into power through conquest, there would certainly be a motive for the later Rus' of Nestor's day to rewrite the official story to make their rule seem more voluntary and thus legitimate)

Another objection is that Nestor writes that "These particular Varangians were known as Rus', just as some are called Swedes, and others Normans and Angles, and still others Gotlanders, for they were thus named." - how could they be Swedes when he listed the Swedes separately? (On the other hand, the Gotlanders are also listed, even though they had been under Swedish rule for some time by then as well)

There is no single 'anti-Normanist' theory. Various (almost all Russian) historians of the 19th century and Soviet era have pointed to other possible origins of the name 'Rus'. At best, they're even more circumstantial than the evidence for the Normanist theory, which is why it hasn't had much support from Western academics.

This earlier thread covers the issue in a pretty comprehensive manner.