WARNING: The following contains spoilers for Episode 5 of The Strongest Sage With The Weakest Crest, "The Strongest Sage Makes Allies," now streaming on Crunchyroll.
Up until now, Matthias "Matty" Hildesheimer has been tight-lipped about the reasons he induced his own reincarnation thousands of years ago when he was still known as Gaius. At best, it's been revealed he fought demons in his past life and was unhappy with his weak single crest -- an aspect of himself he couldn't change in his older incarnation. The goal of obtaining the more powerful four crests was only one reason for his rebirth. The other reason for his reincarnation has yet to be revealed, although Episode 5 dropped some hints that go back to Episode 1.
Looking back, since the start of The Strongest Sage With The Weakest Crest, Matty has consistently shown he always knew more than he let on and consistently outclassed his classmates at everything. He was even invited to teach wordless incantation to his classmates at the Second Academy on his first day of school as a guest instructor. Given his power levels and skillset, it would've made more sense for Matty to have joined the First Academy instead. This is especially true considering he easily bested one of the school's top students, Devilis, who turned out to be a demon in disguise. However, this was a major clue of what he was really after.
As the series progressed, both the Second Academy headmaster and the kingdom's monarch became aware of the presence of infiltrating demons. Since Matty is the newcomer who made the king aware of the demons' silent invasion, he's been leading the initiative to block their entry into the kingdom by creating a magical barrier. He also continued teaching silent incantation to the Second Academy students while he took on the more dangerous tasks of killing dangerous demons to test his new skills.
Another detail that's been gradually revealed over the course of the series is that Matty has all of Gaius' memories and life experiences. This largely explains why he's able to effortlessly defeat powerful demons he shouldn't be able to outclass at his current age; he's been using his past life experiences to his advantage in his newer incarnation. However, despite this, Matty also revealed he's actually weaker in his current incarnation, which is why he's been testing his power levels and skillset against powerful demons whenever he's had the chance; he's been monitoring his own progress.
In Episode 5 of The Strongest Sage, much of what Matty's story arc has been building toward is finally starting to take shape. Beginning with the fact he successfully taught silent incantation at the Second Academy to the point of only needing five students to defeat the entire First Academy, Matty reveals this was his plan all along. Having fulfilled his objective at the school, Matty announces he'll be leaving soon, hinting that the Second Academy was only one of his planned stops.
While Matty still doesn't reveal the other reason he induced his reincarnation, what becomes clear is that he's following demonic auras wherever they present themselves. The fact that he's tracking and killing demons in his current incarnation hints at the real objective of his previous incarnation, Gaius. Nonetheless, this raises more questions than answers: what exactly are the demons planning that Gaius/Matty finds so threatening? If the demons are invading kingdoms, could the demons be planning an invasion of Earth? If so, why is Gaius/Matty determined on facing them alone instead of building an army against them? Does Gaius/Matty have something more to gain from defeating the demons alone? Hopefully, the story provides more answers as the anime progresses.