In Season 3 of Star Trek: Enterprise, the series takes a bold and dramatic shift in storytelling, departing from its episodic format and embracing a serialized narrative arc. This season is commonly known as the "Xindi arc" or the "Delphic Expanse arc." Here's a recap of the main events:

The season begins with a continuation from the Season 2 finale. Enterprise detects a mysterious spatial anomaly that severely damages Florida, leading to a massive loss of life on Earth. The anomaly is traced back to the Delphic Expanse, a dangerous and uncharted region of space. Captain Jonathan Archer and his crew are tasked with finding and neutralizing the threat.

Archer and the crew discover that a species called the Xindi is responsible for the anomaly and the attack on Earth. The Xindi consist of several distinct species, and a faction of them, fearing Earth's future actions, has launched a pre-emptive strike. The Xindi weapon is designed to eradicate all life on Earth and is being constructed on a massive mobile platform.

Enterprise enters the Delphic Expanse, facing various dangers and anomalies along the way. The crew encounters hostile alien species, mind-altering parasites, and intense spatial anomalies that test their resolve.

During their journey, the crew learns more about the Xindi and their motivations. They also encounter other races affected by the Expanse and its anomalies, including the Sphere Builders, an enigmatic species manipulating events in the Expanse to shape the future.

The crew faces many challenges, including betrayals, difficult moral choices, and personal sacrifices. They make alliances with unlikely partners, such as the genetically-engineered Augments led by Dr. Arik Soong, who aid Enterprise in their mission.

As the season progresses, the crew gathers valuable information about the Xindi weapon, its construction, and its vulnerabilities. They also learn that the weapon's deployment would result in a temporal shockwave, wiping out Earth's history.

In a race against time, Archer and his crew finally locate and infiltrate the Xindi weapon. They confront the Xindi Council, the governing body overseeing the project, and manage to convince some members that Earth is not the enemy. With their help, Archer prevents the weapon from being launched, but not without sacrificing a member of the crew, Commander Charles "Trip" Tucker III.

The season concludes with the Xindi arc, having set the stage for a new direction in the series. Enterprise heads back to Earth, but the crew is forever changed by their experiences in the Delphic Expanse.

Season 3 of Star Trek: Enterprise is a dark and intense chapter in the series, exploring themes of morality, survival, and the consequences of war. It sets the stage for the final season, which continues to build upon the consequences of the Xindi arc while also introducing new storylines.

Archer's task of convincing the Xindi not to attack Earth is not an easy one, as the Xindi Council initially sees humanity as a threat. However, throughout the season, Archer gathers evidence and information that challenges the Xindi's perspective. Here are the key elements of Archer's persuasion:

Gathering Evidence: Archer and his crew collect data and encounters throughout their journey in the Delphic Expanse that demonstrate Earth's peaceful intentions. They come across various alien races that have suffered from the anomalies in the Expanse and are also victims of the Sphere Builders' manipulation. Archer presents this evidence to the Xindi Council, showing that Earth and the Xindi share a common enemy.

Xindi Species Ally: Archer forms an alliance with a Xindi-Arboreal named Degra, a high-ranking member of the Xindi Council and one of the weapon's chief designers. Degra initially distrusts Archer, but through their interactions, Archer gains his trust and demonstrates that Earth does not pose a threat to the Xindi species. Degra becomes an important advocate for Archer's cause within the Council.

Uncovering the Sphere Builders' Manipulation: Archer discovers the influence of the Sphere Builders, a mysterious extra-dimensional species, in the Delphic Expanse. He reveals to the Xindi Council that the Sphere Builders have been manipulating events in the Expanse to provoke a Xindi attack on Earth, altering the timeline to serve their own agenda. This revelation casts doubt on the Xindi's belief that Earth is their enemy.

Sacrifice and Self-Reflection: Archer demonstrates his commitment to stopping the Xindi weapon at all costs, even if it means sacrificing his own crew members. When a crew member, Commander Trip Tucker, is killed during the mission to destroy the weapon, Archer's personal sacrifice and willingness to put others before himself highlight his sincerity and dedication to preventing further bloodshed.

Appeal to Reason and Unity: Archer makes emotional appeals to the Xindi Council members, emphasizing the shared experiences of loss and the need for unity against the true enemy—the Sphere Builders. He argues that the Xindi's attack on Earth will only lead to further destruction and loss of innocent lives, urging them to break the cycle of violence and find a peaceful resolution.

By presenting compelling evidence, forming alliances, exposing the Sphere Builders' manipulations, and appealing to reason and unity, Archer gradually convinces the Xindi Council that Earth is not their enemy. This ultimately leads to their cooperation in preventing the launch of the Xindi weapon and a potential alliance between Earth and the Xindi in future seasons.