I'm new to statistics. I want to ask if i have two continuous variables with insignificant correlation between them, but when I converted one of them into binary outcome (according to its cutoff point) and it was entered to logistic regression model as a dependent variable and the other variable as independent variable (continuous) the P value was significant. is it possible? or in other words is it meaningful?
Assuming you're using Pearson's correlation coefficient $\rho$, note that $\rho$ only measures the strength of the linear relationship between your two variables. As such, an insignificant correlation between two variables does not indicate that there is no relationship between the two; merely that a linear relationship between the two variables does not exist.
As such, your $p$-value need not be called into doubt because of the insignificant $\rho$ value.