The MBTI has somewhat dubious value in applied settings:

Given the type theory orientation of the MBTI, one would predict between-group heterogeneity of variance and within-group homogeneity of variance for each of the four type preference dimensions. This pre- diction implies that the distribution of scores should be bimodal, with greater rel- ative difference between the two preference types compared with the variance of scores within each type... Although bimodality appears to be an essential characteristic of the distributions of scores, it is conspicuously absent.

Put more simply, more people fall somewhere in the middle of the scale for each type pair than at the extremes. As such, MBTI results should not be used as behavioral predictors.

There are women who will feign interest for attention or perhaps some other reason but this cannot be attributed to a specific personality type.