Israel's great failures at the golden calf and Beth-peor relegated it to the status of an immature minor son--differing little from that of a slave (4:1). As an immature minor son, Israel was placed under the (temporary) Levitical and Deuteronomic covenants that effected a reconfiguration of its filial relation to God along the lines of a treaty-type covenant. The relationship between God and Israel became characterized as that of a master and his slave (i.e., a suzerain and his vassal).
He then quotes Byrne:
What Paul appears to be doing in using this "immature heir" image is making allowance for a situation where an heir, though long-since designated as such, endures for a time a period of suspension of all legal rights and only later receives the true legal capacity to inherit by having the status of sonship conferred....
Hahn's thesis that Israel's initial status of sonship (Exod. 4:22) was reconfigured to a more servile form by the idolatrous episodes of the golden calf and Beth-peor may also be what was lurking behind Paul's two Old Testament citations in I Corinthians 10. There, in the midst of his warning against apostasy, Paul appeals to these two examples in particular (see vv. 7-8) in order to urge his readers onward in faithfulness. Clearly for Paul, these two events stand out as the paramount examples of Israel's fall, as the forbidden fruit episode did for Adam's.