The obvious question is, 'what did your teachers tell you feudalism was'? It's difficult to unpack this highly idiosyncratic term but you'll find many features of various aspects of the concept of feudalism(s) in many, but not all, medieval societies when viewed from a great height. Almost invariably, when you zoom in, these features become less and less central to the functioning of those societies. So while you have aristocrats, serfs, clergy, and rulers seemingly in the classic triangular hierarchy from a great height, when you zoom into, say, medieval England in the eleventh- through thirteenth-centuries, the power-balance is more conciliar (ie. based around bargaining and communal assent); or society might look like its relationships are dictated by grants of land for military service (ie. fiefs/fees and vassalage, or feudo-vassalic relationships), but when zoomed in you can observe the extension of power through collecting supporters who owed no such tenurial obligations into your affinity - thereby dominating local power structures and institutions such as shire, hundred, and wapentake courts (to use England as an example again).

I'd recommend looking at the sources linked in this post for more information and coming back to this, or they might answer your question entirely.