My understanding is sex is measured by if this individual is going to have a kid will they being the impregnator (male) or the impregnatee (female),

Before we even go in to how this false dichotomy excludes trans people - you've completely erased intersex people.

The bottom line is humans are assigned a sex and gender at birth based almost exclusively on the visible external genitalia, which simply isn't enough to indicate anything other than what external visible genitalia a person has. Beyond that, 95%+ of people are completely unaware of their chromosomes, hormones, or even internal organs, and whether those "match" the sex and gender they were assigned at birth (like cis men with extremely low testosterone, or cis women with XY chromosomes).
When a trans person takes HRT, they are literally changing their biological chemistry, when they have surgery, they are literally changing their physical characteristics, and having XY or XX chromosomes doesn't definitively define anything. If a trans man still has a uterus they can and plenty have gotten pregnant, as men, because being pregnant doesn't invalidate their gender, nor any physical or hormonal changes they might have undergone. Just like not having a uterus doesn't suddenly revoke womanhood (see cis women having hysterectomies).

Both sex and gender are spectrums, and neither are distributed as neatly and bimodally as cis-heteronormative society (and your fourth grade biology teacher) would have you believe.

Trans people are whatever gender they tell you they are, and just like you wouldn't ask cis people for their chromosomal make up to confirm their gender, there is no rational reason to do so to trans people before you accept this (outside of transphobia).

This blog post outlines it better than I can - I like it because it includes links to a variety of primary sources.