It is natural to assume that the Alexamenos graffito is depicting the crucifixion of Christ because we are so accustomed to seeing depictions of the crucifixion of Christ. But in the second and third century that was not the case. For example, in Polybius' Histories, Book 8, chapter 23 it recounts what happened to Achaeus after he was captured by Antiochus :
However the council met, and a long debate ensued
as to what punishment they were to inflict upon Achaeus.
Finally, it was resolved that his extremities should be cut off,
his head severed from his body and sewn up in the skin of an
ass, and his body impaled.
So, who might have been depicted in the Alexamenos graffito? John Henry Middleton wrote in Remains of Ancient Rome, Vol.1, 1892, pp.208, 209 :
One of the most interesting things about this building is the large number of graffiti, or incised inscriptions, which are deeply cut into the plaster. One of these is the rude drawing of a crucified man with the head of an ass or jackal, and a standing figure, apparently in act of adoration, with the rudely scratched inscription, "Alexamenos worships God." This is usually taken to be a caricature of the crucified Christ, but is more probably a scene of Gnostic worship, representing the Egyptian god Anubis. A similar device occurs on certain late Gnostic gems of Egyptian origin.
A German philologist, Richard Wünsch, focused on the Y traced on the right of the crucifix and which has been found on some of the tablets dedicated to the god Set. He concluded that Alexamenos belonged to the sect of the Sethiani. He writes in his book Sethian Curse from Rome, 1898, p.112
[That this is] a symbol from the thought circles of the Sethian Gnosis, is proven by this: to the right of the donkey's head of the Crucified One there is a Y that has not yet been interpreted; it is the same Y that is found on our tablets to the right of the donkey's head of Typhon-Seth and, as stated above, indicates his power over the ways of the underworld.
So, in 2nd/3rd century Rome there were many sects and this crucifixion could have related to several of them. But could it have related to Christianity, as many believe? Perhaps, but there are some problems. There are no depictions of the cross which are clearly Christian elsewhere at this time, and the adulation of the cross only came centuries later. Minucius Felix, who wrote in the latter part of the second century, wrote in the dialogue of Octavius "Crosses, moreover, we [christians] neither worship nor wish for. You [pagans],
indeed, who consecrate gods of wood, adore
wooden crosses perhaps as parts of your gods." That seems the more likely truth of the inscription.