When two objects are rubbed together, they can exchange electrons due to the physical contact between them. This process is known as triboelectric charging.
During the rubbing process, one material tends to attract electrons, while the other material loses electrons. This transfer of electrons results in one object becoming negatively charged (gaining electrons) and the other object becoming positively charged (losing electrons). The specific materials involved determine which one will gain or lose electrons.
The reason they acquire equal and opposite charges is fundamentally due to the conservation of charge. For every electron that is transferred from one object to another, there is a corresponding charge change. Therefore, if one object receives a certain amount of negative charge, the other will have an equal amount of positive charge. Consequently, you end up with two objects that have charges that are equal in magnitude but opposite in nature.