Section 153.003 - No discrimination based on sex or marital status
The court shall consider the qualifications of the parties without regard to their marital status or to the sex of the party or the child in determining which parent to appoint as sole managing conservator, whether to appont a party as joint managing conservator and the terms and conditions of conservatorship and possession of and access to the child.
That said, the term "best interest" is not defined in the Texas Family Code.
Section 153.002 - Best Interest of the child
This section does not provide much guidance to predict the outcome of a case. Discretion of the trial court is extraordinarily broad. It is in the eye of the beholder, the trier of fact, judge or jury.
Lots of fathers get primary custody in the State of Texas. I won't say that is is a slam-dunk or easy. You need a strong, determined, competent family law attorney to show the facts to the judge. But any man that states they cannot get custody merely because they are a male is absolutely wrong. When I litigated approx. half my practice was men seeking custody and I often got it for them. How? Hard work, good facts, good witness and a stable client.