Cowboy Bebop is an anime series from the 1990s that was ahead of its time in terms of storytelling and animation. The series even has an unconventional structure. As an anime that blends the genres of neo-noir, space opera and Western, Cowboy Bebop is largely episodic but also manages to have a central storyline. At the heart of that storyline is Vicious, who is also the series' main antagonist.
At first, it's hard to wrap one's mind around Vicious being the main villain when he barely appears in the series. However, despite the scarcity of physical appearances, Vicious still has a looming presence in the story. His character arc and overall significance all have to do with his relationship with the series protagonist, Spike Spiegel.
Prior to the events of the main series, Spike and Vicious were both members of the Red Dragon Crime Syndicate, an organized crime family. They were both the right-hand men of the Red Dragon's leader, Mao Yenrai, who thought of them as his sons. Spike and Vicious were best friends to the point where they were practically brothers; however, the moment a woman named Julia came between them, their relationship took a nosedive.
On the day of a major gang fight, Spike was severely wounded and left for dead. He was eventually found by Julia who -- at the time -- was Vicious' lover. Julia nursed Spike back to health and the two eventually fell in love. At some point, they pursued a romantic relationship behind Vicious' back and even planned to leave the Red Dragon together to start their lives anew. Tragically for both, Vicious eventually found out about the relationship, which informed his actions from that point forward.
One of Vicious' first actions as a brother-in-arms gone rogue was to threaten Julia with death if she didn't kill Spike to his specifications. The condition he gave was for her to kill Spike at their agreed rendezvous. If she succeeded in her task, he would let her live. If she failed to kill Spike, he would kill them both. Julia ultimately chose not to follow through with Vicious' threat and went into hiding.
Despite failing to eliminate Spike thanks to Julia defying his orders, this didn't stop Vicious from moving forward with his other plan of usurping the Red Dragon Crime Syndicate. He first accomplished this by murdering Mao Yenrai, and later the other elders of the Syndicate. With them out of the picture, Vicious was able to disrupt the new alliances that were formed between crime families, effectively threatening the safety of the entire solar system. He then began funding his reformation of the Red Dragon by selling an illegal performance enhancement drug known as Red Eye.
Vicious nearly succeeded in his coup of the Red Dragon until his murder of Mao Yenrai and subsequent activities on Callisto attracted the attention of Spike. Vicious was able to defeat Spike in their first two encounters in "Ballad of Fallen Angels" and "Jupiter Jazz" Parts 1 and 2. However, once Spike was reunited with Julia, Vicious wasn't so lucky in surviving his third fight. By murdering Julia, Vicious only motivated Spike to go all out on him, eventually putting his own life on the line to ensure Vicious would be stopped once and for all.
Revisiting the question of why Vicious is Cowboy Bebop's main antagonist, it all boils down to two things. First, Vicious has an unresolved history with the series' protagonist. Second, Vicious' usurpation of one of the most powerful crime families in the universe threatens the safety of everyone living in the entire solar system.