They fuck you up, your mum and dad.
This line, which begins Larkin's poem, "This Be the Verse", so forcefully, has long been a puzzlement to scholars, who have debated amongst themselves since its publication what the meaning of "fuck you up" might be. I believe that the key to understanding the line, which recapitulated and varied in the other quatrains (thus giving the poem the structure of a partially-deranged sonata), lies in the preposition, "up". If the speaker of the poem were to have averred that "your mum and dad" merely "fuck you", then the meaning would be clear: the poet would be decrying, or at least pointing out, the incestuous foundations of Western societies since the Greeks. However, as so often happens with words of Germanic origin, here the "up" has the effect of transforming the meaning of the main verb: rather than be a commentary on the direction of fucking, we must recognize that fucking itself has changed. How, one might ask? We look to that most prototypical of "up"-modified verbs: conjure. To fuck something up is to conjure up, or cause to come into existence, by means of fucking. An example with another common verb will put to rest any doubt: for do we not say that one can whip up a PowerPoint presentation, cookies, or military intelligence, meaning thereby that we will create them by means of whipping, respectively, generic business cliches, eggs & flour, or hapless innocents? Thus we see that Larkin here refers to nothing more than biological processes at their most crude: they fuck you up, they beget you. Fuck up a kid or two if you're lamenting your own now-vanished youth.
They may not mean to, but they do.
Larkin here comments on the sad truth: many children are unwanted. Some parents, it is true, make a conscious decision to fuck up kids, and take means to prevent fucking up until they have so decided: they are to be commended. However, others, whether through carelessness, lack of contraceptives or ignorance of their use, religious upbringing, or what-have-you, fuck their kids up willy-nilly, without necessarily even knowing that that's what they're doing.
They fill you with the faults they had
And add some extra, just for you.
The poet's meaning is opaque here. At first, one is tempted to think of cell division in the fertilized egg ("the faults they had"); however, it is difficult to reconcile this with the statement that "some extra" faults are exhibited in the gamete. Indeed, the poem appears to be paradoxical at this point, for how can one be "filled" with a "fault", when a fault is specifically a gap, a that-which-is-unfilled? However, this too can be explained, if we look past the birth: for infants have many more bones, and therefore more "faults", if you will, than an adult, and these bones are created and grow only as the baby takes in calcium from its mother's milk—that is to say, the baby is not so much filled with faults as filled up with faults: faults are created (and then, note, filled, as the baby grows) by means of a filling with milk.
But they were fucked up in their turn
By fools in old-style hats and coats,
Who half the time were soppy-stern
And half at one another's throats.
The first two lines of this quatrain are nothing more than the aforementioned recapitulation of what might be called the main theme, biological reproduction. Note, however, that although it is a recapitulation, that which it describes properly speaking happens before what is described in the first quatrain, thus demonstrating the defamiliarizing uses to which Larkin puts the flow of time. (Much interesting work remains to be done in this area.)
The final two lines, I'm pretty sure, are oral sex references of various sorts.
Man hands on misery to man.
It deepens like a coastal shelf.
Here we see an instance of Larkin's fondness for employing common words in uncommon senses. "Misery" here refers, of course, to the sixth definition in the OED, "bodily pain or discomfort"; notably, one of the illustrative quotations is "Lizy's took bad with a misery in her stomach"—that is, Lizy's pregnant. "Man hands on misery to man" calls attention to that which is not present, the pregnant woman, whose belly "deepens" as the gamete grows, just as does the tree of sexual reproduction, leading all the way back into the sea, whence our first ancestors emerged (thus showing the aptness of the simile).
Interestingly, manuscript drafts reveal that the original of the first line of this quatrain was to have been "Man hands inhumanity to man", showing that, for all that this poem is deeply concerned with biology, for a good while Larkin himself was ironically uninformed on the subject, and hewed to an outmoded homuncular theory of reproduction, "in-humanity" here being synecdochic for "sperm", on the principle that it is the little human living in the sperm that gives it its vital force.
Get out as early as you can,
And don't have any kids yourself.
The variation on the theme, coming after the statement and recapitulation, is meant to show the derangement of those who would issue such a call.