A stream winner is not capable of creating schism and taking another teacher, because a stream winner has verified confidence (i.e. conviction resulting from experiential realization) in the Buddha, the Dhamma (his teachings) and the Sangha (the monastic community).
From the Vera Sutta:
"And which are the four factors of stream-entry with which he is
"There is the case where the disciple of the noble ones is endowed
with verified confidence in the Awakened One: 'Indeed, the Blessed One
is worthy & rightly self-awakened, consummate in knowledge & conduct,
well-gone, an expert with regard to the world, unexcelled as a trainer
for those people fit to be tamed, the Teacher of divine & human
beings, awakened, blessed.'
"He is endowed with verified confidence in the Dhamma: 'The Dhamma is
well-expounded by the Blessed One, to be seen here & now, timeless,
inviting verification, pertinent, to be realized by the wise for
"He is endowed with verified confidence in the Sangha: 'The Sangha of
the Blessed One's disciples who have practiced well... who have
practiced straight-forwardly... who have practiced methodically... who
have practiced masterfully — in other words, the four pairs, the eight
individuals  — they are the Sangha of the Blessed One's disciples:
worthy of gifts, worthy of hospitality, worthy of offerings, worthy of
respect, the incomparable field of merit for the world.'
The Sangha referred above is composed of eight types of individuals:
The four pairs are (1) the person on the path to stream-entry, the
person experiencing the fruit of stream-entry; (2) the person on the
path to once-returning, the person experiencing the fruit of
once-returning; (3) the person on the path to non-returning, the
person experiencing the fruit of non-returning; (4) the person on the
path to arahantship, the person experiencing the fruit of arahantship.
The eight individuals are the eight types forming these four pairs.
It doesn't say that those are offences. It says that a stream winner is not capable of these acts. Since a stream winner is fully convinced in the Buddha and his teachings, he is not capable of taking another teacher. A stream winner has also reached the level of spiritual maturity that makes him incapable of committing matricide, patricide and murder of an enlightened person.
Not just matricide, patricide and killing arahant, according to the Cakkhu Sutta, the stream winner "is incapable of doing any deed by which he might be reborn in hell, in the animal womb, or in the realm of hungry shades." Also in this verse, The Buddha said "the sotapannas do not kill, they do not wish others to get killed."