| Quote #1
I was lying when I said just now that I was a spiteful official. I was lying from spite. (1.1.5)
This is some classic existential absurdity going on here. If he's lying from spite, it must mean that he's spiteful. The Underground man introduces this type of logic (or illogic?) early in the text, setting the stage for the "reasoning" that is to follow.
| Quote #2
How much better it is to understand it all, to recognise it all, all the impossibilities and the stone wall; not to be reconciled to one of those impossibilities and stone walls if it disgusts you to be reconciled to it; by the way of the most inevitable, logical combinations to reach the most revolting conclusions on the everlasting theme, that even for the stone wall you are yourself somehow to blame, though again it is as clear as day you are not to blame in the least (1.3.7)
Jean-Paul Sartre would later continue this idea of radical personal freedom; every man is free – completely. It's not that you're not prevented in any way from committing murder; technically, you can. It's just that you don't want to face the consequences. The downside, however, is that you are responsible for everything that happens to you. When the Underground Man talks about being to blame for everything – even the laws of nature that you really can't do anything about – he is creating an the early premise for this later concept.
| Quote #3
[…] to sink into luxurious inertia, brooding on the fact that there is no one even for you to feel vindictive against, that you have not, and perhaps never will have, an object for your spite, that it is a sleight of hand, a bit of juggling, a card-sharper's trick, that it is simply a mess, no knowing what and no knowing who, but in spite of all these uncertainties and jugglings, still there is an ache in you, and the more you do not know, the worse the ache. (1.3.7)
Some existentialists believed that there was no such thing as objective truth. Similarly, the Underground Man suffers from the uncertainty of his knowledge of everything. He constantly second-guesses himself.