Your male rabbit will rub his chin on everything as it's a natural behavior called chinning where the rabbit is marking his territory by depositing his scent from the rabbits scent glands that are located under the rabbits chin.
When the male rabbit rubs his chin on things he's essentially claiming the objects or areas as his own and it's a way to let other rabbits know to stay away from those objects or areas.
Every rabbit has scent glands that are located underneath their chin which secrete a subtle odor that is undetectable to humans but is a big deal in the world of rabbits.
Male and female rabbits will also fight for a variety of reasons which include establishing their dominance within their relationship and even for competing for food and other resources if the resources are scarce.
Male and female rabbits may also fight due to mating related aggression, especially when the female rabbit is not receptive or due to hormonal changes as a result of sexual maturity, stress from environmental changes or improper introductions when they're not properly bonded.
It's crucial to neuter rabbits to minimize any fighting by reducing hormonal influences on the rabbits behavior.
Rabbits are not rodents as rabbits are mammals that are in the order of Lagomorpha.
Lagomorpha also includes pikas and hares.
On the other hand rodents are in a separate order called Rodentia which includes marmots, squirrels, rats and mice.
Rabbits also have 2 sets of upper incisors and rodents only have one set of incisors.
A rabbits incisors are also larger and more prominent than rodents incisors and has a smaller set of peg like teeth behind them.
Rabbits are also herbivores which eat grasses, leaves and other plant matter and their digestive system is adapted to high fiber diets.
Although until the early 20th century, rabbits and lagomorphs were classified as rodents but rabbits are not rodents at all.