categorical independent variable with three levels and binary logistic regression

I want to learn which level of a categorical independent variable should I look to interpret the odd ratios in binary logistic regression. For example, I have one independent categorical variable (education ) with three levels. The results of binary logistic regression show that "edu" (reference level) is not significant but one of the levels is significant "edu(2)".

Is it possible to ignore the overall significance of "edu" and interpret the "edu(2)"?

You should be very careful with that! We need to know what the three levels of edu signifies, and how that categorical variable is encoded. The most used encoding is dummy variables (also known as "one-hot"). In that case, the two estimated parameters that you see, represents difference to the reference level. Do you really want to test the hypothesis that that difference is zero?