P-value rejecting alt hypothesis when it shouldn't

-------------Belief in Afterlife

Gender------Yes---No---Total

Female------509---116---625

Male--------398---104---502

Test the claim that the proportion of females who believe in an afterlife is larger than the proportion of males.

Null Hypothesis= Ho: p1=p2

Alternative Hypothesis= Ho: p1>p2

My z score was 0.9080619

My p-value was 0.1819

The significance level was 0.05

Now here is my problem, since the p-value is greater then the significance level then I would fail to reject aka accept the null hypothesis and reject the alternative hypothesis. This means that the proportion of women who believe in the afterlife is NOT greater then men who do. HOWEVER by doing simple calculations from the data table above the proportion of women is .81 where is the proportion of men is .79. Why would my p-value say something that isn't true in the first place?

and no my p-value is correct as well as my z-score according to my statcrunch computer program.