(This took way too long to type)
I first and foremost wanted to make this post in order to compare the arguments from both sides (Naruto dodged the beam vs Naruto dodged the swing) and to create counterarguments to those saying Naruto dodged the swing. I'll be breaking down the main arguments and comparing them to the counterarguments. (Edit: Took me a while to figure out how to collapse this thing. sorry for any inconvenience)
Madara tilts his head when activating his Rinnega
I've already explained this one earlier, but any apparent "tilt" of Madara's head can easily be explained as the artist emphasizing Madara's Rinnegan activation. The evidence is in Chapter 415 of the Naruto manga in which Sasuke activates his Mangekyo Sharingan's Amaterasu on Bee and you can easily see the emphasis placed on his Sharingan as he does so; the same emphasis that is placed on Madara's Rinnegan.
——————————————————————————————————————————————————
Naruto about to swing down on Madara
This panel is a very important one because this is where the argument that Naruto dodged the swing germinates from. The idea is that using perspective lines to measure Naruto's and Madara's perspective in relation to each other, you can see that Madara's head is tilted to Naruto's right.
Few Responses:
The anime does not really contradict that scan and the perspectives of the characters in both instances are similar. Since this is true and since the anime makes it evident that Naruto dodged the beam, then it would likewise be possible for the same thing to have occurred in the scan.
Of course, some may not like me trying to compare the anime to the manga (even though it doesn't contradict it at any point), so we'll go to response 2 and 3 which have to do with the scans where Naruto is stopped by Madara's Limbo clone.
The 2 panels after Madara activates his limbo clone, features Naruto being stopped mid-air by the Limbo clone.
First and foremost, the perspective lines in the panel where Naruto and Madara are facing each other are different from that of the panel where Naruto's staff is raised, but that's not really my main argument. My response comes from the fact that in the panel below the ones with the perspective lines, it is evident that Naruto's staff is not to the right of his body or anything, but it is actually centered. Do you see how his arm comes into the center of his body (shown by the diagonal line)? This indicates that the staff is actually held in the center of his body. This is easily testable by anyone. Just put your arm out and across from you and you'll see that it's centered. Now, this is important because, in the panel prior, Naruto and Madara are facing each other head-on and so if Naruto's staff is centered, then that's evidence to suggest that they were facing each other directly. Additionally, if (in the panel where they are facing each other) Madara's head was as tilted away from Naruto as the perspective lines make it out to be, then we wouldn't even be seeing half his face in the bottom panel as his head would be slightly turned away.
Finally, in order to say that Madara's head was turned away from Naruto in the bottom panel, you would have to assume that nothing changed in between the time that Naruto's staff was raised to the time that Naruto's staff was brought down. This isn't quite logical as someone explained "Madara is a tactical genius. He isn't tilting his head to the side just to prep his beam when he can just fire it and pierce Naruto's head straight up, and then swing his head for added effect. It just doesn't make sense." However, this is just my headcanon and should not be taken as direct evidence against the Anti-SoL statements laid out (even though they too are headcanon)
————————————————————————————————————————
Naruto's Headband
The claim here is that is is impossible for a beam fired towards the center of Naruto's head to somehow manage to slice both the right and left top sides of the headband.
Few Replies:
Not contradicted by the anime, but I know a lot of you don't like that.
After Madara fired the beam, Naruto dodged and tilted his head to the right placing his headbands in the perfect position to get cut. Madara, realizing his attack missed, swung causing the beam to slice the headbands. Basically "the momentum of Naruto dodging to the side and down would send the headbands upwards and in the line of Madara's head slice". But, someone will say headcanon (even though both arguments are founded on headcanon as everyone is interpreting the manga in their own way.)
Lastly, in this image you can clearly see a piece of Naruto's "headband" flaking off from the rest of it. Now, am I seriously suggesting that Naruto's headband just started falling off for no reason? No, it is quite evident that it's just Naruto's energy wafting off his form...something completely uncontradicted in the anime as seen when Madara cuts his "headband".
——————————————————————————————————————————————————
The direction Naruto's staff flew after being cut
The argument for Naruto dodging the swing here is that the direction which the Naruto's staff is cut suggests Madara swung from left to right.
Few replies:
[Insert "Anime doesn't contradict the manga" statement]. Moving on.
Naruto's sudden movement tilted the rod away and in addition to the fact that it was already in front of him, it is reasonable to conclude that that is the reason why is diverted to the side. (My headcanon again).
I've already stated how Naruto's staff was aligned in the center of his body while he was being stopped by Madara's limbo and that Madara was facing him directly. Thing is, even if Madara's head was turned even a centimeter away from the staff before he fired the beam, his sudden motion would still be in line to pierce through Naruto's head and his swing could still cause the staff to get cut in that manner. (Also my interpretation of the events i.e. headcanon, but so is everyone's interpretation of these scans)
———————————————————————————————————————— Honorable Mentions:
Claim 1: Naruto is more than competent enough to realize that dodging the head swing rather than the beam itself would be much easier and less dangerous than dodging the beam itself.
Reply 1: Naruto doesn't get to decide whether to dodge the beam or the swing...either Madara shot the beam at Naruto or near him. Naruto simply reacted to one situation or the other.
Claim 2: Motion lines
Reply 2: Can be explained in favor of both situations. Look back at the OP
———————————————————————————————————————— For every argument against Naruto dodging the beam, there is a corresponding argument for it. Why does this matter? It means that multiple interpretations can be derived from the manga and neither side has enough evidence to conclusively say Naruto dodged the swing and the beam. Because we are dealing with two positive claims: Naruto dodged the swing vs Naruto dodged the beam, both sides have to deliver evidence to support their claims. Now, if both scenarios are equally as likely and the anime doesn't contradict the scans during any of the scans of that fight thus far, it should be used to solve the invisible scenario in the manga; whatever happened in between Madara firing his beam and Naruto dodging.
In conclusion: Two positive claims are being made: Naruto dodged Madara's swing and Naruto dodged Madara's beam. Both sides need enough evidence to support their claim.
Neither side has enough evidence based on the scans alone to come to a definite conclusion regarding whether Naruto dodged the swing or the beam.
The anime in no way contradicts any of the scenes that occurred in the Manga panels so it should be used as supporting evidence
Since the above is true and both conclusions can be reached by the scans, the Anime technically doesn't contradict the manga in the sense that it clearly showed Naruto dodging the beam; one of the two scenarios that could be concluded based on the manga.