I don't think that's the case

Matthew 19:12 NRSV [12] For there are eunuchs who have been so from birth, and there are eunuchs who have been made eunuchs by others, and there are eunuchs who have made themselves eunuchs for the sake of the kingdom of heaven. Let anyone accept this who can.”

Jesus mentions two types of eunuchs here. Those who are made, and those who are born as eunuchs. The latter, those who are born as eunuchs are what we today call intersex people.

Intersex people have ambiguous sex characteristics and are born that way. Intersex people make up around 1.7% of the population, around the same amount as people who have red hair. They are pretty distinct. Sometimes they can have male genitalia and female sex hormones, while still others can have ambiguous genitalia. Others still have male chromosomes when being phenotypically female.

Not every one of these was included in the term Eunuch, as they aren't always visible traits. But many of these traits were visible so they were seen as distinct from men. Oftentimes they're born that way.

(An aside while it's on my mind, Jesus tells us that marriage is overrated in this passage. I think we neglect our single church members a lot, seeing as there doesn't seem to be much space for them outside of the context of marriage. And this passage says that marriage isn't for everyone)