Ni isn't directly irrational, it just has a hard time coming to explain the rationale behind its conclusions. INFJs are particularly good at picking up little symbols and patterns in the behavior of others that most types won't recognize...but then not being able to explain why they understood something so subtle and unknowable by others.
So there is a reason Ni types come to their conclusion, it's just tough for them to explain why.
Fe is similar to the pattern recognizing of Ni, except Fe is like a database. Ni recognizes the symbols and patterns, and then checks it against the Fe database to come to conclusions. Fe is about understanding how a person feels by how their dress, expressions, etc match up against the cultural (and individual if the INFJ has familiarity with this person) norm for which emotion they may be feeling.
So in that sense INFJs are not irrational, they just have to develop the ability to explain their conclusions (Ti). They have to learn to be able to later pick apart what normally just comes so naturally to them. Underdeveloped INFJs can be a frustration for others, as they basically do the "just believe what I say, even though I have little evidence/explanation" routine.