When Jesus says that the scribes and Pharisees sit in Moses' seat, he invokes an image of recognized authority in teaching Israel's law. The statement is immediately followed by a warning not to imitate teachers whose behavior fails to match what they teach.
The image therefore combines respect for the authority associated with Moses and sharp criticism of hypocrisy.
In Jewish communities, Scripture was read and interpreted by recognized teachers. The expression 'Moses' seat' naturally evokes authority derived from Moses and the Torah. Archaeological synagogue seats sometimes called 'Moses' seats' show that prominent teaching seats existed, although individual finds should not be used to reconstruct one universal first-century arrangement.
Matthew's emphasis is functional: the scribes and Pharisees occupy a position associated with teaching, while Jesus evaluates how that authority is exercised.
The background keeps the passage from becoming either blanket rejection or blanket endorsement of religious leaders. Jesus can acknowledge the weight of Torah teaching while condemning inconsistency between instruction and practice.
The saying therefore turns attention toward accountable leadership: possessing a recognized teaching role does not excuse failure to live according to what is taught.