I swear levi and hanji's bond is just so pure. it's really something special and I would never get tired of saying this. most people would probably think that they wouldn't work well together in the long run because "they are too different" but they aren't actually that different? from what we have scene right at the moment they were introduced they are already close. right from the start isayama established that yes these two characters are friends. yes they have different personalities—levi is quiet and reserved while hanji is energetic. levi likes cleaning and it is said that hanji forgets to take care of their hygiene. but that's not all there is to their characters! also if you ask me I think hanji being unhygienic is just something that got blown way out of proportion because of the existing side materials. I don't remember this ever being addressed in the manga or anime? I think that hanji just gets too distracted with their work that they would sometimes forget to take showers. it's not that they hate being clean but rather they don't want to get taken away from their research. I don't think levi resents them for that either? it seems to me that he is worried about hanji's health that's why he has taken it upon himself to remind them to bathe.
if you look at their characters on suface value, they look like complete opposite. but if you look deeper, you would notice how similar they are. both have the same penchant for shit jokes. hanj is the only character we've seen respond to levi's jokes and the only one who dares to challenge levi's occasional sarcastic remarks. the two also share similar ideologies and are very compassionate and selfless people. they strongly value life—a common theme about levi is how always tells his comrades before battle to not die. one of the aspects of his character arcs is to give meanings to the deaths of his fallen comrades. whenever hanji makes plans or inventions what they always keep in mind is to minimize deaths. hanji was able to achieve that through the invention of executioner from hell. under hanji's command the scouts were able to wipe out the titans in the island by while avoiding casualties. they carried the wills of their comrades. levi and hanji both believed that the rumbling isn't something that their comrades would want. they are two of the very few characters who were shown to be vocally against the rumbling.
another set of similarities they have is how the two are regarded as different. hanji is often seen as eccentric because of their genius while levi is socially awkward and easily misunderstood. hanji is viewed as odd for their unconventional ideas and even though levi might tease them sometimes, it is undeniable that levi highly values their insights and acknowledges that they are an intelligent individual. levi is often misunderstood because of how crude he speaks at times but hanji sees way past that and knows of the kind mind behind that facade.
all these similarities are what allowed them to have that very deep understanding. that understading between them is consistently developed throughout the series. you can see it with the way they talk during missions and how comfortable they are with each other's presence. they are each other's confidants because they know they would never judge the other. need proof? just read 126. that deep level of understanding is the strongest aspect of their bond—it's what allowed them to let go of each other. that's where their love manifests.
