How does Taxi Driver relate to belonging?
The notion of belonging is extremely important to the film's main idea and themes. Travis is fundamentally on the outside looking in. When he says that he feels like "God's lonely man," it is a statement of how alienated he is from the social setting in which he is emerged. He struggles to find a place of belonging in this setting. The coffee shop where he hangs out with other caddies is a potential area where some belonging could be evident. This is seen when he steps outside to talk to Wizard about "some bad things" that are on his mind. His attempts to belong are futile, though, when Wizard simply tells him to "go get laid." Travis sojourns in his cab and in his life to find some level of belonging or acceptance. His attempts to be with Betsy, commit himself to Palatine or Kris Kristofferson albums, or even join the Secret Service as "Henry Krinkle" are all vain attempts to belong. The only real acceptance he finds is through violence. The killing of Sport and the other exploiters of girls like Iris, intended to be his own death, is the domain where belonging is evident. It becomes a strange twist that this self- destructive attempt at inclusion is what he receives praise for at the end, truly reflective of how much of a lack of synchronicity and belonging exists between Travis and his world.
One might also note that Travis once belonged to a "killer elite" as evidenced by the jacket he wore, he was once not just a US Marine, but part of Marine Force Recon, which is an elite within the elite. If the Marines are tough, then the members of Force Recon are tough Marines.
However, he is no longer a member. He is now a civilian where the rules are almost entirely different.
Humans generally derive meaning in their life from the associations they make and keep, but as pointed out in the first answer above, Travis is not very successful at this. He is used to structure and discipline, without which he seemly drifts. He is now a Ronin, a 'wave man' tossed about by the currents of society (to use the literal Japanese meaning of the term).
In Feudal Japan, the Ronin were masterless samurai who attempted to find a new path in life. If they were lucky they might regain a position serving a Clan, or give up their swords and became merchants or farmers. Most, however, fell back upon their stock in trade, the use of violence, and became hired swords or criminals.
Travis, having left the Marines (for reasons unknown) is trying to find a new path. He contemplates rejoining a Clan (the Secret Service) while trying his hand at being a 'merchant' but in the end he falls back upon the one trade he knows, and knows very well, the use of violence.
It is this skill, this 'talent' that earned him a place with his former clan (Marines), and now gains him the respect that grants him entrée as a favored member into his new clan (Cabbies).