In disagreement, opposed. For example, It is only natural
for the young and old to be at odds over money matters. This idiom
uses odds in the sense of “a condition of being unequal or different,”
and transfers it to a difference of opinion, or quarrel. [Late 1500s ]
The American Heritage® Idioms
Being "at odds" is contrasted with being "edgy, dangerous" which is actually confirmed by modern science.
When the central nervous system is released from the depressed state,
the opposite state develops-feeling edgy and irritable. Missouri
Department of Mental Health
Further, the most common drug which causes this sort of depression described in the quotation above is alcohol.
So tying all of these together in this particular instance saying "at odds with everything" means to remain depressed, drunk - because he remains not happy with the world and thus has a reason to keep drinking and remain in a depressed state - whereas if he were to fall in love maybe he wouldn't want to drink and that would bring him out of his depression and, as medical science will support, would cause him to go into another extreme state of being edgy, irratable and potentially even dangerous. He concludes by saying that to stay in a depressed state is the correct perspective - that the world is ultimately unhappy (and what is implied is that to fall in love risks losing that perspective and then becoming edgy and even dangerous especially when the brief illusion of happiness will ultimately be shattered by the reality - the correct perspecive - that the world is unhappy).