As a side note, the structure of the saying in Matthew 19:11f is strongly reminiscent of 13:11f:
Not everyone accepts (lit. "make room for") this (variant, the) word, but those to whom it is given (dedotai). 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 (idem) this who can.
... Let anyone with ears listen!
Then the disciples came and asked him, "Why do you speak to them in parables?" He answered, "To you it has been given (dedotai) to know the secrets of the kingdom of heaven, but to them it has not been given(dedotai). For to those who have, more will be given (dothèsetai), and they will have an abundance; but from those who have nothing, even what they have will be taken away. The reason I speak to them in parables is that 'seeing they do not perceive, and hearing they do not listen, nor do they understand.' With them indeed is fulfilled the prophecy of Isaiah that says: 'You will indeed listen, but never understand, and you will indeed look, but never perceive...
It is characteristic of mysterious, esoterical teaching which is offered to the inner circle of disciples (as is even in clearer in Mark 4, cf. v. 10, 33f).
Now the notion of "gift" can also refer to the kharisma in 1 Corinthians 7:7...
Anyway, before the rejection of Gnosticism in the Pastorals, Christianity doesn't seem to have been strongly committed to "marriage and family values" as many now hold it to be.